LMFDB - Embedded newform 462.2.n.e.65.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(65,462)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("462.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.9
Character	$\chi$	$=$	462.65
Dual form			462.2.n.e.263.9

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.783456 - 1.54473i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.23623 + 1.86844i) q^{5} +(0.946049 + 1.45086i) q^{6} +(0.830341 - 2.51208i) q^{7} +1.00000 q^{8} +(-1.77239 - 2.42046i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.783456 - 1.54473i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.23623 + 1.86844i) q^{5} +(0.946049 + 1.45086i) q^{6} +(0.830341 - 2.51208i) q^{7} +1.00000 q^{8} +(-1.77239 - 2.42046i) q^{9} +(-3.23623 + 1.86844i) q^{10} +(1.70984 - 2.84191i) q^{11} +(-1.72951 + 0.0938734i) q^{12} +4.64070i q^{13} +(1.76035 + 1.97514i) q^{14} +(5.42167 - 3.53527i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.460807 + 0.798142i) q^{17} +(2.98238 - 0.324709i) q^{18} +(-4.14430 - 2.39271i) q^{19} -3.73687i q^{20} +(-3.22995 - 3.25076i) q^{21} +(1.60625 + 2.90172i) q^{22} +(-4.94452 - 2.85472i) q^{23} +(0.783456 - 1.54473i) q^{24} +(4.48211 + 7.76324i) q^{25} +(-4.01896 - 2.32035i) q^{26} +(-5.12755 + 0.841552i) q^{27} +(-2.59069 + 0.536942i) q^{28} +7.73875 q^{29} +(0.350793 + 6.46294i) q^{30} +(1.26564 + 2.19216i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.05041 - 4.86775i) q^{33} -0.921615 q^{34} +(7.38083 - 6.57821i) q^{35} +(-1.20998 + 2.74517i) q^{36} +(-1.29412 + 2.24149i) q^{37} +(4.14430 - 2.39271i) q^{38} +(7.16863 + 3.63578i) q^{39} +(3.23623 + 1.86844i) q^{40} +4.10460 q^{41} +(4.43021 - 1.17184i) q^{42} -2.19681i q^{43} +(-3.31609 - 0.0598058i) q^{44} +(-1.21340 - 11.1448i) q^{45} +(4.94452 - 2.85472i) q^{46} +(4.96151 + 2.86453i) q^{47} +(0.946049 + 1.45086i) q^{48} +(-5.62107 - 4.17176i) q^{49} -8.96422 q^{50} +(1.59394 - 0.0865151i) q^{51} +(4.01896 - 2.32035i) q^{52} +(3.30063 - 1.90562i) q^{53} +(1.83497 - 4.86137i) q^{54} +(10.8433 - 6.00235i) q^{55} +(0.830341 - 2.51208i) q^{56} +(-6.94298 + 4.52725i) q^{57} +(-3.86938 + 6.70196i) q^{58} +(-7.65662 + 4.42055i) q^{59} +(-5.77247 - 2.92767i) q^{60} +(6.52747 + 3.76863i) q^{61} -2.53129 q^{62} +(-7.55207 + 2.44259i) q^{63} +1.00000 q^{64} +(-8.67085 + 15.0184i) q^{65} +(5.74080 - 0.207858i) q^{66} +(0.390387 + 0.676170i) q^{67} +(0.460807 - 0.798142i) q^{68} +(-8.28358 + 5.40141i) q^{69} +(2.00648 + 9.68109i) q^{70} +11.4978i q^{71} +(-1.77239 - 2.42046i) q^{72} +(-9.35455 + 5.40085i) q^{73} +(-1.29412 - 2.24149i) q^{74} +(15.5037 - 0.841502i) q^{75} +4.78543i q^{76} +(-5.71935 - 6.65500i) q^{77} +(-6.73300 + 4.39033i) q^{78} +(-14.9095 - 8.60802i) q^{79} +(-3.23623 + 1.86844i) q^{80} +(-2.71724 + 8.58001i) q^{81} +(-2.05230 + 3.55469i) q^{82} +12.6784 q^{83} +(-1.20026 + 4.42260i) q^{84} +3.44396i q^{85} +(1.90249 + 1.09840i) q^{86} +(6.06297 - 11.9543i) q^{87} +(1.70984 - 2.84191i) q^{88} +(-7.44976 - 4.30112i) q^{89} +(10.2583 + 4.52155i) q^{90} +(11.6578 + 3.85336i) q^{91} +5.70943i q^{92} +(4.37787 - 0.237621i) q^{93} +(-4.96151 + 2.86453i) q^{94} +(-8.94127 - 15.4867i) q^{95} +(-1.72951 + 0.0938734i) q^{96} -12.1684 q^{97} +(6.42339 - 2.78211i) q^{98} +(-9.90923 + 0.898400i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 8 q^{9}+O(q^{10}) $ 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 8 * q^9	$ 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 8 q^{9} - 4 q^{11} + 4 q^{15} - 12 q^{16} + 4 q^{17} - 8 q^{18} + 8 q^{22} + 20 q^{25} - 12 q^{27} + 40 q^{29} - 2 q^{30} - 28 q^{31} - 12 q^{32} + 32 q^{33} - 8 q^{34} - 32 q^{35} + 16 q^{36} - 16 q^{37} - 8 q^{41} + 6 q^{42} - 4 q^{44} - 28 q^{45} - 8 q^{49} - 40 q^{50} - 34 q^{51} + 6 q^{54} + 8 q^{55} + 40 q^{57} - 20 q^{58} - 2 q^{60} + 56 q^{62} - 14 q^{63} + 24 q^{64} - 44 q^{65} + 32 q^{66} + 4 q^{68} - 20 q^{69} + 64 q^{70} - 8 q^{72} - 16 q^{74} - 26 q^{75} + 24 q^{81} + 4 q^{82} + 144 q^{83} - 6 q^{84} + 8 q^{87} - 4 q^{88} + 56 q^{90} - 32 q^{91} - 22 q^{93} - 44 q^{95} + 64 q^{97} - 8 q^{98} - 52 q^{99}+O(q^{100}) $ 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 8 * q^9 - 4 * q^11 + 4 * q^15 - 12 * q^16 + 4 * q^17 - 8 * q^18 + 8 * q^22 + 20 * q^25 - 12 * q^27 + 40 * q^29 - 2 * q^30 - 28 * q^31 - 12 * q^32 + 32 * q^33 - 8 * q^34 - 32 * q^35 + 16 * q^36 - 16 * q^37 - 8 * q^41 + 6 * q^42 - 4 * q^44 - 28 * q^45 - 8 * q^49 - 40 * q^50 - 34 * q^51 + 6 * q^54 + 8 * q^55 + 40 * q^57 - 20 * q^58 - 2 * q^60 + 56 * q^62 - 14 * q^63 + 24 * q^64 - 44 * q^65 + 32 * q^66 + 4 * q^68 - 20 * q^69 + 64 * q^70 - 8 * q^72 - 16 * q^74 - 26 * q^75 + 24 * q^81 + 4 * q^82 + 144 * q^83 - 6 * q^84 + 8 * q^87 - 4 * q^88 + 56 * q^90 - 32 * q^91 - 22 * q^93 - 44 * q^95 + 64 * q^97 - 8 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.783456	−	1.54473i	0.452328	−	0.891851i
$3$	0.783456	−	1.54473i	0.452328	−	0.891851i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	3.23623	+	1.86844i	1.44728	+	0.835590i	0.998319	−	0.0579588i	$-0.0184592\pi$
$5$	3.23623	+	1.86844i	1.44728	+	0.835590i	0.448966	+	0.893549i	$0.351793\pi$
$6$	0.946049	+	1.45086i	0.386223	+	0.592311i
$7$	0.830341	−	2.51208i	0.313839	−	0.949476i
$7$	0.830341	−	2.51208i	0.313839	−	0.949476i
$8$	1.00000			0.353553
$9$	−1.77239	−	2.42046i	−0.590798	−	0.806819i
$10$	−3.23623	+	1.86844i	−1.02338	+	0.590852i
$11$	1.70984	−	2.84191i	0.515535	−	0.856869i
$11$	1.70984	−	2.84191i	0.515535	−	0.856869i
$12$	−1.72951	+	0.0938734i	−0.499265	+	0.0270989i
$13$			4.64070i			1.28710i	0.765405	+	0.643549i	$0.222539\pi$
$13$			4.64070i			1.28710i	−0.765405	+	0.643549i	$0.777461\pi$
$14$	1.76035	+	1.97514i	0.470474	+	0.527877i
$15$	5.42167	−	3.53527i	1.39987	−	0.912802i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.460807	+	0.798142i	0.111762	+	0.193578i	0.916481	−	0.400079i	$-0.131017\pi$
$17$	0.460807	+	0.798142i	0.111762	+	0.193578i	−0.804719	+	0.593656i	$0.797684\pi$
$18$	2.98238	−	0.324709i	0.702953	−	0.0765347i
$19$	−4.14430	−	2.39271i	−0.950768	−	0.548926i	−0.0574485	−	0.998348i	$-0.518296\pi$
$19$	−4.14430	−	2.39271i	−0.950768	−	0.548926i	−0.893319	+	0.449422i	$0.851630\pi$
$20$		−	3.73687i		−	0.835590i
$21$	−3.22995	−	3.25076i	−0.704833	−	0.709373i
$22$	1.60625	+	2.90172i	0.342454	+	0.618648i
$23$	−4.94452	−	2.85472i	−1.03100	−	0.595250i	−0.113731	−	0.993512i	$-0.536280\pi$
$23$	−4.94452	−	2.85472i	−1.03100	−	0.595250i	−0.917272	+	0.398262i	$0.869614\pi$
$24$	0.783456	−	1.54473i	0.159922	−	0.315317i
$25$	4.48211	+	7.76324i	0.896422	+	1.55265i
$26$	−4.01896	−	2.32035i	−0.788183	−	0.455058i
$27$	−5.12755	+	0.841552i	−0.986798	+	0.161957i
$28$	−2.59069	+	0.536942i	−0.489595	+	0.101473i
$29$	7.73875			1.43705			0.718525	−	0.695501i	$-0.244818\pi$
$29$	7.73875			1.43705			0.718525	+	0.695501i	$0.244818\pi$
$30$	0.350793	+	6.46294i	0.0640458	+	1.17997i
$31$	1.26564	+	2.19216i	0.227316	+	0.393723i	0.957012	−	0.290049i	$-0.0936715\pi$
$31$	1.26564	+	2.19216i	0.227316	+	0.393723i	−0.729696	+	0.683772i	$0.760338\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−3.05041	−	4.86775i	−0.531008	−	0.847367i
$34$	−0.921615			−0.158056
$35$	7.38083	−	6.57821i	1.24759	−	1.11192i
$36$	−1.20998	+	2.74517i	−0.201664	+	0.457528i
$37$	−1.29412	+	2.24149i	−0.212752	+	0.368498i	−0.952575	−	0.304304i	$-0.901576\pi$
$37$	−1.29412	+	2.24149i	−0.212752	+	0.368498i	0.739823	+	0.672802i	$0.234909\pi$
$38$	4.14430	−	2.39271i	0.672294	−	0.388149i
$39$	7.16863	+	3.63578i	1.14790	+	0.582191i
$40$	3.23623	+	1.86844i	0.511692	+	0.295426i
$41$	4.10460			0.641030			0.320515	−	0.947243i	$-0.396144\pi$
$41$	4.10460			0.641030			0.320515	+	0.947243i	$0.396144\pi$
$42$	4.43021	−	1.17184i	0.683597	−	0.180819i
$43$		−	2.19681i		−	0.335010i	−0.985871	−	0.167505i	$-0.946429\pi$
$43$		−	2.19681i		−	0.335010i	0.985871	−	0.167505i	$-0.0535711\pi$
$44$	−3.31609	−	0.0598058i	−0.499919	−	0.00901607i
$45$	−1.21340	−	11.1448i	−0.180883	−	1.66136i
$46$	4.94452	−	2.85472i	0.729029	−	0.420905i
$47$	4.96151	+	2.86453i	0.723711	+	0.417835i	0.816117	−	0.577887i	$-0.196122\pi$
$47$	4.96151	+	2.86453i	0.723711	+	0.417835i	−0.0924058	+	0.995721i	$0.529456\pi$
$48$	0.946049	+	1.45086i	0.136550	+	0.209413i
$49$	−5.62107	−	4.17176i	−0.803010	−	0.595966i
$50$	−8.96422			−1.26773
$51$	1.59394	−	0.0865151i	0.223196	−	0.0121145i
$52$	4.01896	−	2.32035i	0.557330	−	0.321774i
$53$	3.30063	−	1.90562i	0.453377	−	0.261757i	−0.255878	−	0.966709i	$-0.582365\pi$
$53$	3.30063	−	1.90562i	0.453377	−	0.261757i	0.709255	+	0.704952i	$0.249031\pi$
$54$	1.83497	−	4.86137i	0.249708	−	0.661548i
$55$	10.8433	−	6.00235i	1.46212	−	0.809357i
$56$	0.830341	−	2.51208i	0.110959	−	0.335690i
$57$	−6.94298	+	4.52725i	−0.919620	+	0.599649i
$58$	−3.86938	+	6.70196i	−0.508074	+	0.880010i
$59$	−7.65662	+	4.42055i	−0.996807	+	0.575507i	−0.907302	−	0.420480i	$-0.861862\pi$
$59$	−7.65662	+	4.42055i	−0.996807	+	0.575507i	−0.0895048	+	0.995986i	$0.528528\pi$
$60$	−5.77247	−	2.92767i	−0.745222	−	0.377961i
$61$	6.52747	+	3.76863i	0.835756	+	0.482524i	0.855819	−	0.517275i	$-0.173053\pi$
$61$	6.52747	+	3.76863i	0.835756	+	0.482524i	−0.0200632	+	0.999799i	$0.506387\pi$
$62$	−2.53129			−0.321474
$63$	−7.55207	+	2.44259i	−0.951472	+	0.307737i
$64$	1.00000			0.125000
$65$	−8.67085	+	15.0184i	−1.07549	+	1.86280i
$66$	5.74080	−	0.207858i	0.706644	−	0.0255855i
$67$	0.390387	+	0.676170i	0.0476934	+	0.0826073i	0.888887	−	0.458127i	$-0.151480\pi$
$67$	0.390387	+	0.676170i	0.0476934	+	0.0826073i	−0.841193	+	0.540735i	$0.818146\pi$
$68$	0.460807	−	0.798142i	0.0558811	−	0.0967889i
$69$	−8.28358	+	5.40141i	−0.997226	+	0.650253i
$70$	2.00648	+	9.68109i	0.239821	+	1.15711i
$71$			11.4978i			1.36454i	0.731100	+	0.682271i	$0.239007\pi$
$71$			11.4978i			1.36454i	−0.731100	+	0.682271i	$0.760993\pi$
$72$	−1.77239	−	2.42046i	−0.208879	−	0.285254i
$73$	−9.35455	+	5.40085i	−1.09487	+	0.632122i	−0.934868	−	0.354995i	$-0.884482\pi$
$73$	−9.35455	+	5.40085i	−1.09487	+	0.632122i	−0.159999	+	0.987117i	$0.551149\pi$
$74$	−1.29412	−	2.24149i	−0.150439	−	0.260567i
$75$	15.5037	−	0.841502i	1.79021	−	0.0971683i
$76$			4.78543i			0.548926i
$77$	−5.71935	−	6.65500i	−0.651781	−	0.758407i
$78$	−6.73300	+	4.39033i	−0.762362	+	0.497107i
$79$	−14.9095	−	8.60802i	−1.67745	−	0.968478i	−0.963276	−	0.268514i	$-0.913467\pi$
$79$	−14.9095	−	8.60802i	−1.67745	−	0.968478i	−0.714178	−	0.699964i	$-0.753199\pi$
$80$	−3.23623	+	1.86844i	−0.361821	+	0.208898i
$81$	−2.71724	+	8.58001i	−0.301915	+	0.953335i
$82$	−2.05230	+	3.55469i	−0.226638	+	0.392549i
$83$	12.6784			1.39163			0.695816	−	0.718220i	$-0.255043\pi$
$83$	12.6784			1.39163			0.695816	+	0.718220i	$0.255043\pi$
$84$	−1.20026	+	4.42260i	−0.130959	+	0.482545i
$85$			3.44396i			0.373550i
$86$	1.90249	+	1.09840i	0.205151	+	0.118444i
$87$	6.06297	−	11.9543i	0.650019	−	1.28164i
$88$	1.70984	−	2.84191i	0.182269	−	0.302949i
$89$	−7.44976	−	4.30112i	−0.789673	−	0.455918i	0.0501742	−	0.998740i	$-0.484022\pi$
$89$	−7.44976	−	4.30112i	−0.789673	−	0.455918i	−0.839848	+	0.542822i	$0.817356\pi$
$90$	10.2583	+	4.52155i	1.08132	+	0.476613i
$91$	11.6578	+	3.85336i	1.22207	+	0.403942i
$92$			5.70943i			0.595250i
$93$	4.37787	−	0.237621i	0.453964	−	0.0246401i
$94$	−4.96151	+	2.86453i	−0.511741	+	0.295454i
$95$	−8.94127	−	15.4867i	−0.917354	−	1.58890i
$96$	−1.72951	+	0.0938734i	−0.176517	+	0.00958092i
$97$	−12.1684			−1.23551			−0.617756	−	0.786370i	$-0.711958\pi$
$97$	−12.1684			−1.23551			−0.617756	+	0.786370i	$0.711958\pi$
$98$	6.42339	−	2.78211i	0.648860	−	0.281035i
$99$	−9.90923	+	0.898400i	−0.995915	+	0.0902926i
$100$	4.48211	−	7.76324i	0.448211	−	0.776324i
$101$	−0.661912	−	1.14646i	−0.0658627	−	0.114077i	0.831214	−	0.555953i	$-0.187647\pi$
$101$	−0.661912	−	1.14646i	−0.0658627	−	0.114077i	−0.897076	+	0.441876i	$0.854313\pi$
$102$	−0.722045	+	1.42365i	−0.0714931	+	0.140962i
$103$	−4.94954	+	8.57285i	−0.487693	+	0.844708i	−0.999900	−	0.0141536i	$-0.995495\pi$
$103$	−4.94954	+	8.57285i	−0.487693	+	0.844708i	0.512207	+	0.858862i	$0.328828\pi$
$104$			4.64070i			0.455058i
$105$	−4.37902	−	16.5551i	−0.427349	−	1.61562i
$106$			3.81124i			0.370181i
$107$	−5.61684	+	9.72865i	−0.543000	+	0.940504i	0.455730	+	0.890118i	$0.349378\pi$
$107$	−5.61684	+	9.72865i	−0.543000	+	0.940504i	−0.998730	+	0.0503857i	$0.983955\pi$
$108$	3.29258	+	4.01981i	0.316829	+	0.386807i
$109$	−3.95986	+	2.28623i	−0.379286	+	0.218981i	−0.677508	−	0.735516i	$-0.736940\pi$
$109$	−3.95986	+	2.28623i	−0.379286	+	0.218981i	0.298221	+	0.954497i	$0.403607\pi$
$110$	−0.223487	+	12.3918i	−0.0213086	+	1.18151i
$111$	2.44861	+	3.75518i	0.232412	+	0.356426i
$112$	1.76035	+	1.97514i	0.166338	+	0.186633i
$113$		−	7.52223i		−	0.707632i	−0.935315	−	0.353816i	$-0.884884\pi$
$113$		−	7.52223i		−	0.707632i	0.935315	−	0.353816i	$-0.115116\pi$
$114$	−0.449224	−	8.27642i	−0.0420737	−	0.775158i
$115$	−10.6677	−	18.4770i	−0.994770	−	1.72299i
$116$	−3.86938	−	6.70196i	−0.359263	−	0.622261i
$117$	11.2326	−	8.22514i	1.03846	−	0.760415i
$118$		−	8.84110i		−	0.813889i
$119$	2.38762	−	0.494854i	0.218873	−	0.0453632i
$120$	5.42167	−	3.53527i	0.494929	−	0.322724i
$121$	−5.15292	−	9.71841i	−0.468447	−	0.883491i
$122$	−6.52747	+	3.76863i	−0.590969	+	0.341196i
$123$	3.21577	−	6.34050i	0.289956	−	0.571704i
$124$	1.26564	−	2.19216i	0.113658	−	0.196862i
$125$			14.8138i			1.32499i
$126$	1.66069	−	7.76158i	0.147946	−	0.691456i
$127$			5.14870i			0.456873i	0.973559	+	0.228437i	$0.0733614\pi$
$127$			5.14870i			0.456873i	−0.973559	+	0.228437i	$0.926639\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−3.39348	−	1.72110i	−0.298779	−	0.151535i
$130$	−8.67085	−	15.0184i	−0.760484	−	1.31720i
$131$	−7.91279	+	13.7053i	−0.691343	+	1.19744i	0.280054	+	0.959984i	$0.409647\pi$
$131$	−7.91279	+	13.7053i	−0.691343	+	1.19744i	−0.971398	+	0.237458i	$0.923686\pi$
$132$	−2.69039	+	5.07561i	−0.234168	+	0.441775i
$133$	−9.45186	+	8.42404i	−0.819581	+	0.730457i
$134$	−0.780774			−0.0674486
$135$	−18.1663	−	6.85705i	−1.56351	−	0.590161i
$136$	0.460807	+	0.798142i	0.0395139	+	0.0684401i
$137$	11.1932	−	6.46241i	0.956302	−	0.552121i	0.0612689	−	0.998121i	$-0.480485\pi$
$137$	11.1932	−	6.46241i	0.956302	−	0.552121i	0.895033	+	0.446000i	$0.147152\pi$
$138$	−0.535964	−	9.87450i	−0.0456243	−	0.840573i
$139$		−	8.08854i		−	0.686061i	−0.939324	−	0.343031i	$-0.888547\pi$
$139$		−	8.08854i		−	0.686061i	0.939324	−	0.343031i	$-0.111453\pi$
$140$	−9.38731	−	3.10288i	−0.793373	−	0.262241i
$141$	8.31206	−	5.41998i	0.700002	−	0.456444i
$142$	−9.95741	−	5.74892i	−0.835608	−	0.482438i
$143$	13.1885	+	7.93483i	1.10287	+	0.663544i
$144$	2.98238	−	0.324709i	0.248531	−	0.0270591i
$145$	25.0444	+	14.4594i	2.07982	+	1.20079i
$146$		−	10.8017i		−	0.893955i
$147$	−10.8481	+	5.41465i	−0.894737	+	0.446593i
$148$	2.58824			0.212752
$149$	6.60066	−	11.4327i	0.540747	−	0.936602i	−0.458114	−	0.888893i	$-0.651475\pi$
$149$	6.60066	−	11.4327i	0.540747	−	0.936602i	0.998861	−	0.0477082i	$-0.0151917\pi$
$150$	−7.02307	+	13.8473i	−0.573431	+	1.13063i
$151$	−10.3132	+	5.95435i	−0.839279	+	0.484558i	−0.857019	−	0.515285i	$-0.827686\pi$
$151$	−10.3132	+	5.95435i	−0.839279	+	0.484558i	0.0177403	+	0.999843i	$0.494353\pi$
$152$	−4.14430	−	2.39271i	−0.336147	−	0.194075i
$153$	1.11514	−	2.52999i	0.0901535	−	0.204537i
$154$	8.62307	−	1.62561i	0.694867	−	0.130995i
$155$			9.45910i			0.759773i
$156$	−0.435638	−	8.02611i	−0.0348790	−	0.642603i
$157$	6.04984	+	10.4786i	0.482830	+	0.836286i	0.999806	−	0.0197142i	$-0.00627562\pi$
$157$	6.04984	+	10.4786i	0.482830	+	0.836286i	−0.516976	+	0.856000i	$0.672942\pi$
$158$	14.9095	−	8.60802i	1.18614	−	0.684818i
$159$	−0.357774	−	6.59157i	−0.0283734	−	0.522745i
$160$		−	3.73687i		−	0.295426i
$161$	−11.2769	+	10.0506i	−0.888745	+	0.792100i
$162$	−6.07189	−	6.64320i	−0.477053	−	0.521939i
$163$	0.770417	−	1.33440i	0.0603437	−	0.104518i	−0.834275	−	0.551348i	$-0.814114\pi$
$163$	0.770417	−	1.33440i	0.0603437	−	0.104518i	0.894619	+	0.446830i	$0.147447\pi$
$164$	−2.05230	−	3.55469i	−0.160258	−	0.277574i
$165$	−0.776738	−	21.4526i	−0.0604690	−	1.67009i
$166$	−6.33919	+	10.9798i	−0.492016	+	0.852197i
$167$	10.2207			0.790902			0.395451	−	0.918487i	$-0.370588\pi$
$167$	10.2207			0.790902			0.395451	+	0.918487i	$0.370588\pi$
$168$	−3.22995	−	3.25076i	−0.249196	−	0.250801i
$169$	−8.53607			−0.656621
$170$	−2.98256	−	1.72198i	−0.228752	−	0.132070i
$171$	1.55387	+	14.2719i	0.118828	+	1.09140i
$172$	−1.90249	+	1.09840i	−0.145064	+	0.0837525i
$173$	3.49761	−	6.05803i	0.265918	−	0.460584i	−0.701886	−	0.712290i	$-0.747658\pi$
$173$	3.49761	−	6.05803i	0.265918	−	0.460584i	0.967804	+	0.251706i	$0.0809916\pi$
$174$	7.32124	+	11.2278i	0.555022	+	0.851180i
$175$	23.2235	−	4.81327i	1.75554	−	0.363849i
$176$	1.60625	+	2.90172i	0.121076	+	0.218725i
$177$	0.829944	+	15.2907i	0.0623824	+	1.14932i
$178$	7.44976	−	4.30112i	0.558383	−	0.322383i
$179$	−20.0703	+	11.5876i	−1.50012	+	0.866097i	−0.500125	+	0.865953i	$0.666713\pi$
$179$	−20.0703	+	11.5876i	−1.50012	+	0.866097i	−1.00000		0.000143992i	$0.999954\pi$
$180$	−9.04495	+	6.62321i	−0.674170	+	0.493665i
$181$	−6.34142			−0.471354			−0.235677	−	0.971831i	$-0.575731\pi$
$181$	−6.34142			−0.471354			−0.235677	+	0.971831i	$0.575731\pi$
$182$	−9.16601	+	8.16926i	−0.679430	+	0.605546i
$183$	10.9355	−	7.13063i	0.808376	−	0.527111i
$184$	−4.94452	−	2.85472i	−0.364515	−	0.210453i
$185$	−8.37615	+	4.83597i	−0.615827	+	0.355548i
$186$	−1.98315	+	3.91016i	−0.145412	+	0.286707i
$187$	3.05615	+	0.0551180i	0.223488	+	0.00403062i
$188$		−	5.72906i		−	0.417835i
$189$	−2.14357	+	13.5796i	−0.155922	+	0.987769i
$190$	17.8825			1.29734
$191$	6.08888	+	3.51541i	0.440576	+	0.254366i	0.703842	−	0.710357i	$-0.251466\pi$
$191$	6.08888	+	3.51541i	0.440576	+	0.254366i	−0.263266	+	0.964723i	$0.584800\pi$
$192$	0.783456	−	1.54473i	0.0565410	−	0.111481i
$193$	−7.54828	+	4.35800i	−0.543337	+	0.313696i	−0.746430	−	0.665464i	$-0.768234\pi$
$193$	−7.54828	+	4.35800i	−0.543337	+	0.313696i	0.203093	+	0.979159i	$0.434901\pi$
$194$	6.08419	−	10.5381i	0.436819	−	0.756593i
$195$	16.4061	+	25.1604i	1.17487	+	1.80177i
$196$	−0.802319	+	6.95387i	−0.0573085	+	0.496705i
$197$	0.556764			0.0396678			0.0198339	−	0.999803i	$-0.493686\pi$
$197$	0.556764			0.0396678			0.0198339	+	0.999803i	$0.493686\pi$
$198$	4.17658	−	9.03085i	0.296817	−	0.641794i
$199$	3.23869	+	5.60958i	0.229585	+	0.397653i	0.957685	−	0.287818i	$-0.0929298\pi$
$199$	3.23869	+	5.60958i	0.229585	+	0.397653i	−0.728100	+	0.685471i	$0.759597\pi$
$200$	4.48211	+	7.76324i	0.316933	+	0.548944i
$201$	1.35035	−	0.0732939i	0.0952465	−	0.00516975i
$202$	1.32382			0.0931439
$203$	6.42580	−	19.4403i	0.451003	−	1.36444i
$204$	−0.871893	−	1.33713i	−0.0610447	−	0.0936180i
$205$	13.2834	+	7.66918i	0.927754	+	0.535639i
$206$	−4.94954	−	8.57285i	−0.344851	−	0.597299i
$207$	1.85391	+	17.0277i	0.128855	+	1.18351i
$208$	−4.01896	−	2.32035i	−0.278665	−	0.160887i
$209$	−13.8860	+	7.68659i	−0.960512	+	0.531692i
$210$	16.5267	+	4.48523i	1.14045	+	0.309510i
$211$		−	17.8142i		−	1.22638i	−0.789936	−	0.613189i	$-0.789886\pi$
$211$		−	17.8142i		−	1.22638i	0.789936	−	0.613189i	$-0.210114\pi$
$212$	−3.30063	−	1.90562i	−0.226688	−	0.130879i
$213$	17.7611	+	9.00804i	1.21697	+	0.617221i
$214$	−5.61684	−	9.72865i	−0.383959	−	0.665037i
$215$	4.10460	−	7.10937i	0.279931	−	0.484855i
$216$	−5.12755	+	0.841552i	−0.348886	+	0.0572603i
$217$	6.55779	−	1.35916i	0.445172	−	0.0922655i
$218$		−	4.57246i		−	0.309686i
$219$	1.01399	+	18.6816i	0.0685193	+	1.26239i
$220$	−10.6199	−	6.38944i	−0.715991	−	0.430776i
$221$	−3.70394	+	2.13847i	−0.249154	+	0.143849i
$222$	−4.47638	+	0.242967i	−0.300435	+	0.0163069i
$223$	9.10963			0.610026			0.305013	−	0.952348i	$-0.401339\pi$
$223$	9.10963			0.610026			0.305013	+	0.952348i	$0.401339\pi$
$224$	−2.59069	+	0.536942i	−0.173098	+	0.0358760i
$225$	10.8465	−	24.6083i	0.723103	−	1.64055i
$226$	6.51444	+	3.76112i	0.433334	+	0.250186i
$227$	12.5369	+	21.7145i	0.832101	+	1.44124i	0.896369	+	0.443308i	$0.146195\pi$
$227$	12.5369	+	21.7145i	0.832101	+	1.44124i	−0.0642687	+	0.997933i	$0.520471\pi$
$228$	7.39220	+	3.74917i	0.489561	+	0.248295i
$229$	11.5525	−	20.0095i	0.763408	−	1.32226i	−0.177676	−	0.984089i	$-0.556858\pi$
$229$	11.5525	−	20.0095i	0.763408	−	1.32226i	0.941084	−	0.338173i	$-0.109809\pi$
$230$	21.3354			1.40682
$231$	−14.7610	+	3.62097i	−0.971206	+	0.238243i
$232$	7.73875			0.508074
$233$	−11.6393	+	20.1599i	−0.762517	+	1.32072i	0.179033	+	0.983843i	$0.442703\pi$
$233$	−11.6393	+	20.1599i	−0.762517	+	1.32072i	−0.941549	+	0.336875i	$0.890630\pi$
$234$	1.50688	+	13.8403i	0.0985076	+	0.904769i
$235$	10.7044	+	18.5406i	0.698278	+	1.20945i
$236$	7.65662	+	4.42055i	0.498403	+	0.287753i
$237$	−24.9780	+	16.2872i	−1.62250	+	1.05797i
$238$	−0.765255	+	2.31517i	−0.0496041	+	0.150070i
$239$	−2.95273			−0.190996			−0.0954981	−	0.995430i	$-0.530444\pi$
$239$	−2.95273			−0.190996			−0.0954981	+	0.995430i	$0.530444\pi$
$240$	0.350793	+	6.46294i	0.0226436	+	0.417181i
$241$	3.18416	−	1.83837i	0.205110	−	0.118420i	−0.393927	−	0.919142i	$-0.628884\pi$
$241$	3.18416	−	1.83837i	0.205110	−	0.118420i	0.599037	+	0.800722i	$0.295550\pi$
$242$	10.9928	+	0.396643i	0.706647	+	0.0254971i
$243$	11.1250	+	10.9195i	0.713668	+	0.700484i
$244$		−	7.53727i		−	0.482524i
$245$	−10.3964	−	24.0034i	−0.664200	−	1.53352i
$246$	3.88315	+	5.95519i	0.247581	+	0.379689i
$247$	11.1039	−	19.2324i	0.706522	−	1.22373i
$248$	1.26564	+	2.19216i	0.0803685	+	0.139202i
$249$	9.93294	−	19.5847i	0.629475	−	1.24113i
$250$	−12.8291	−	7.40689i	−0.811385	−	0.468453i
$251$		−	27.0815i		−	1.70937i	−0.519147	−	0.854685i	$-0.673750\pi$
$251$		−	27.0815i		−	1.70937i	0.519147	−	0.854685i	$-0.326250\pi$
$252$	5.89138	+	5.31899i	0.371122	+	0.335065i
$253$	−16.5672	+	9.17078i	−1.04157	+	0.576562i
$254$	−4.45890	−	2.57435i	−0.279777	−	0.161529i
$255$	5.31999	+	2.69819i	0.333151	+	0.168967i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−12.5519	−	7.24684i	−0.782965	−	0.452045i	0.0545147	−	0.998513i	$-0.482639\pi$
$257$	−12.5519	−	7.24684i	−0.782965	−	0.452045i	−0.837480	+	0.546468i	$0.815972\pi$
$258$	3.18726	−	2.07829i	0.198430	−	0.129389i
$259$	4.55622	+	5.11213i	0.283110	+	0.317653i
$260$	17.3417			1.07549
$261$	−13.7161	−	18.7313i	−0.849006	−	1.15944i
$262$	−7.91279	−	13.7053i	−0.488854	−	0.846719i
$263$	−7.25088	−	12.5589i	−0.447108	−	0.774414i	0.551088	−	0.834447i	$-0.314213\pi$
$263$	−7.25088	−	12.5589i	−0.447108	−	0.774414i	−0.998196	+	0.0600330i	$0.980879\pi$
$264$	−3.05041	−	4.86775i	−0.187740	−	0.299589i
$265$	14.2421			0.874887
$266$	−2.56950	−	12.3976i	−0.157546	−	0.760144i
$267$	−12.4806	+	8.13815i	−0.763803	+	0.498047i
$268$	0.390387	−	0.676170i	0.0238467	−	0.0413037i
$269$	6.66567	−	3.84843i	0.406413	−	0.234643i	−0.282834	−	0.959169i	$-0.591275\pi$
$269$	6.66567	−	3.84843i	0.406413	−	0.234643i	0.689248	+	0.724526i	$0.257941\pi$
$270$	15.0215	−	12.3040i	0.914182	−	0.748795i
$271$	2.86928	+	1.65658i	0.174296	+	0.100630i	0.584610	−	0.811314i	$-0.301248\pi$
$271$	2.86928	+	1.65658i	0.174296	+	0.100630i	−0.410314	+	0.911944i	$0.634581\pi$
$272$	−0.921615			−0.0558811
$273$	15.0858	−	14.9892i	0.913033	−	0.907189i
$274$			12.9248i			0.780817i
$275$	29.7261	+	0.536113i	1.79255	+	0.0323288i
$276$	8.81955	+	4.47309i	0.530874	+	0.269248i
$277$	−7.75856	+	4.47940i	−0.466166	+	0.269141i	−0.714634	−	0.699499i	$-0.753407\pi$
$277$	−7.75856	+	4.47940i	−0.466166	+	0.269141i	0.248467	+	0.968640i	$0.420073\pi$
$278$	7.00488	+	4.04427i	0.420125	+	0.242559i
$279$	3.06281	−	6.94881i	0.183366	−	0.416014i
$280$	7.38083	−	6.57821i	0.441089	−	0.393123i
$281$	22.9477			1.36894			0.684471	−	0.729040i	$-0.260033\pi$
$281$	22.9477			1.36894			0.684471	+	0.729040i	$0.260033\pi$
$282$	0.537807	+	9.90844i	0.0320259	+	0.590039i
$283$	22.4674	−	12.9715i	1.33555	−	0.771078i	0.349402	−	0.936973i	$-0.386385\pi$
$283$	22.4674	−	12.9715i	1.33555	−	0.771078i	0.986143	+	0.165895i	$0.0530513\pi$
$284$	9.95741	−	5.74892i	0.590864	−	0.341135i
$285$	−30.9279	+	1.67869i	−1.83201	+	0.0994373i
$286$	−13.4660	+	7.45412i	−0.796261	+	0.440771i
$287$	3.40822	−	10.3111i	0.201181	−	0.608643i
$288$	−1.20998	+	2.74517i	−0.0712988	+	0.161761i
$289$	8.07531	−	13.9869i	0.475018	−	0.822756i
$290$	−25.0444	+	14.4594i	−1.47066	+	0.849083i
$291$	−9.53339	+	18.7969i	−0.558857	+	1.10189i
$292$	9.35455	+	5.40085i	0.547434	+	0.316061i
$293$	−5.56705			−0.325230			−0.162615	−	0.986690i	$-0.551993\pi$
$293$	−5.56705			−0.325230			−0.162615	+	0.986690i	$0.551993\pi$
$294$	0.734831	−	12.1021i	0.0428562	−	0.705807i
$295$	−33.0381			−1.92355
$296$	−1.29412	+	2.24149i	−0.0752193	+	0.130284i
$297$	−6.37566	+	16.0110i	−0.369953	+	0.929050i
$298$	6.60066	+	11.4327i	0.382366	+	0.662277i
$299$	13.2479	−	22.9460i	0.766145	−	1.32700i
$300$	−8.48059	−	13.0058i	−0.489627	−	0.750891i
$301$	−5.51855	−	1.82410i	−0.318084	−	0.105139i
$302$		−	11.9087i		−	0.685268i
$303$	−2.28956	+	0.124272i	−0.131532	+	0.00713923i
$304$	4.14430	−	2.39271i	0.237692	−	0.137232i
$305$	14.0829	+	24.3923i	0.806385	+	1.39670i
$306$	1.63346	+	2.23073i	0.0933790	+	0.127522i
$307$			30.2069i			1.72400i	0.506909	+	0.862000i	$0.330788\pi$
$307$			30.2069i			1.72400i	−0.506909	+	0.862000i	$0.669212\pi$
$308$	−2.90372	+	8.28060i	−0.165455	+	0.471831i
$309$	9.36502	+	14.3622i	0.532757	+	0.817035i
$310$	−8.19182	−	4.72955i	−0.465264	−	0.268620i
$311$	−0.793092	+	0.457892i	−0.0449721	+	0.0259647i	−0.522318	−	0.852751i	$-0.674932\pi$
$311$	−0.793092	+	0.457892i	−0.0449721	+	0.0259647i	0.477345	+	0.878716i	$0.341599\pi$
$312$	7.16863	+	3.63578i	0.405844	+	0.205836i
$313$	2.87594	−	4.98127i	0.162558	−	0.281558i	−0.773228	−	0.634129i	$-0.781359\pi$
$313$	2.87594	−	4.98127i	0.162558	−	0.281558i	0.935785	+	0.352571i	$0.114692\pi$
$314$	−12.0997			−0.682825
$315$	−29.0040	−	6.20581i	−1.63419	−	0.349658i
$316$			17.2160i			0.968478i
$317$	−9.09364	−	5.25022i	−0.510750	−	0.294882i	0.222392	−	0.974957i	$-0.428614\pi$
$317$	−9.09364	−	5.25022i	−0.510750	−	0.294882i	−0.733142	+	0.680076i	$0.761947\pi$
$318$	5.88735	+	2.98594i	0.330146	+	0.167443i
$319$	13.2320	−	21.9928i	0.740850	−	1.23136i
$320$	3.23623	+	1.86844i	0.180911	+	0.104449i
$321$	10.6276	+	16.2985i	0.593175	+	0.909692i
$322$	−3.06564	−	14.7914i	−0.170841	−	0.824292i
$323$		−	4.41032i		−	0.245397i
$324$	8.78913	−	1.93681i	0.488285	−	0.107601i
$325$	−36.0269	+	20.8001i	−1.99841	+	1.15378i
$326$	0.770417	+	1.33440i	0.0426695	+	0.0739057i
$327$	0.429232	+	7.90809i	0.0237366	+	0.437318i
$328$	4.10460			0.226638
$329$	11.3157	−	10.0852i	0.623853	−	0.556013i
$330$	18.9669	+	10.0536i	1.04409	+	0.553435i
$331$	7.54164	−	13.0625i	0.414526	−	0.717981i	−0.580852	−	0.814009i	$-0.697281\pi$
$331$	7.54164	−	13.0625i	0.414526	−	0.717981i	0.995379	+	0.0960284i	$0.0306140\pi$
$332$	−6.33919	−	10.9798i	−0.347908	−	0.602594i
$333$	7.71912	−	0.840427i	0.423005	−	0.0460551i
$334$	−5.11035	+	8.85139i	−0.279626	+	0.484327i
$335$			2.91765i			0.159408i
$336$	4.43021	−	1.17184i	0.241688	−	0.0639292i
$337$		−	14.8370i		−	0.808223i	−0.914710	−	0.404111i	$-0.867581\pi$
$337$		−	14.8370i		−	0.808223i	0.914710	−	0.404111i	$-0.132419\pi$
$338$	4.26804	−	7.39246i	0.232151	−	0.402097i
$339$	−11.6198	−	5.89333i	−0.631103	−	0.320082i
$340$	2.98256	−	1.72198i	0.161752	−	0.0933874i
$341$	8.39397	+	0.151386i	0.454559	+	0.00819800i
$342$	−13.1368	−	5.79028i	−0.710357	−	0.313102i
$343$	−15.1472	+	10.6566i	−0.817872	+	0.575401i
$344$		−	2.19681i		−	0.118444i
$345$	−36.8997	+	2.00283i	−1.98662	+	0.107829i
$346$	3.49761	+	6.05803i	0.188033	+	0.325682i
$347$	0.849785	+	1.47187i	0.0456188	+	0.0790141i	0.887933	−	0.459972i	$-0.152141\pi$
$347$	0.849785	+	1.47187i	0.0456188	+	0.0790141i	−0.842314	+	0.538987i	$0.818807\pi$
$348$	−13.3842	+	0.726463i	−0.717469	+	0.0389425i
$349$		−	20.1684i		−	1.07959i	−0.841796	−	0.539796i	$-0.818502\pi$
$349$		−	20.1684i		−	1.07959i	0.841796	−	0.539796i	$-0.181498\pi$
$350$	−7.44336	+	22.5188i	−0.397864	+	1.20368i
$351$	−3.90539	−	23.7954i	−0.208454	−	1.27011i
$352$	−3.31609	−	0.0598058i	−0.176748	−	0.00318766i
$353$	−9.88903	+	5.70943i	−0.526340	+	0.303883i	−0.739525	−	0.673129i	$-0.764950\pi$
$353$	−9.88903	+	5.70943i	−0.526340	+	0.303883i	0.213185	+	0.977012i	$0.431616\pi$
$354$	−13.6571	−	6.92661i	−0.725868	−	0.368145i
$355$	−21.4830	+	37.2096i	−1.14020	+	1.97488i
$356$			8.60225i			0.455918i
$357$	1.10618	−	4.07593i	0.0585452	−	0.215721i
$358$		−	23.1752i		−	1.22485i
$359$	4.22498	−	7.31788i	0.222986	−	0.386223i	−0.732727	−	0.680522i	$-0.761753\pi$
$359$	4.22498	−	7.31788i	0.222986	−	0.386223i	0.955713	+	0.294299i	$0.0950862\pi$
$360$	−1.21340	−	11.1448i	−0.0639516	−	0.587380i
$361$	1.95015	+	3.37776i	0.102640	+	0.177777i
$362$	3.17071	−	5.49183i	0.166649	−	0.288644i
$363$	−19.0494	+	0.345941i	−0.999835	+	0.0181572i
$364$	−2.49179	−	12.0226i	−0.130605	−	0.630157i
$365$	−40.3646			−2.11278
$366$	0.707549	+	13.0357i	0.0369842	+	0.681389i
$367$	−0.156031	−	0.270253i	−0.00814474	−	0.0141071i	0.861924	−	0.507037i	$-0.169259\pi$
$367$	−0.156031	−	0.270253i	−0.00814474	−	0.0141071i	−0.870069	+	0.492930i	$0.835926\pi$
$368$	4.94452	−	2.85472i	0.257751	−	0.148812i
$369$	−7.27496	−	9.93501i	−0.378720	−	0.517196i
$370$		−	9.67194i		−	0.502820i
$371$	−2.04642	−	9.87376i	−0.106245	−	0.512620i
$372$	−2.39472	−	3.67254i	−0.124161	−	0.190412i
$373$	−29.1559	−	16.8331i	−1.50963	−	0.871587i	−0.999937	−	0.0112328i	$-0.996424\pi$
$373$	−29.1559	−	16.8331i	−1.50963	−	0.871587i	−0.509696	−	0.860354i	$-0.670242\pi$
$374$	−1.57581	+	2.61915i	−0.0814832	+	0.135433i
$375$	22.8833	+	11.6059i	1.18169	+	0.599329i
$376$	4.96151	+	2.86453i	0.255871	+	0.147727i
$377$			35.9132i			1.84962i
$378$	−10.6885	−	8.64618i	−0.549756	−	0.444712i
$379$	8.97243			0.460883			0.230441	−	0.973086i	$-0.425983\pi$
$379$	8.97243			0.460883			0.230441	+	0.973086i	$0.425983\pi$
$380$	−8.94127	+	15.4867i	−0.458677	+	0.794452i
$381$	7.95336	+	4.03378i	0.407463	+	0.206657i
$382$	−6.08888	+	3.51541i	−0.311534	+	0.179864i
$383$	6.48945	+	3.74669i	0.331596	+	0.191447i	0.656549	−	0.754283i	$-0.272015\pi$
$383$	6.48945	+	3.74669i	0.331596	+	0.191447i	−0.324954	+	0.945730i	$0.605349\pi$
$384$	0.946049	+	1.45086i	0.0482779	+	0.0740388i
$385$	−6.07469	−	32.2233i	−0.309595	−	1.64225i
$386$		−	8.71600i		−	0.443633i
$387$	−5.31728	+	3.89361i	−0.270293	+	0.197923i
$388$	6.08419	+	10.5381i	0.308878	+	0.534992i
$389$	−9.97406	+	5.75853i	−0.505705	+	0.291969i	−0.731066	−	0.682306i	$-0.760977\pi$
$389$	−9.97406	+	5.75853i	−0.505705	+	0.291969i	0.225361	+	0.974275i	$0.427644\pi$
$390$	−29.9926	+	1.62792i	−1.51873	+	0.0824332i
$391$		−	5.26190i		−	0.266106i
$392$	−5.62107	−	4.17176i	−0.283907	−	0.210706i
$393$	14.9718	+	22.9607i	0.755226	+	1.15821i
$394$	−0.278382	+	0.482171i	−0.0140247	+	0.0242914i
$395$	−32.1671	−	55.7150i	−1.61850	−	2.80333i
$396$	5.73265	+	8.13245i	0.288077	+	0.408671i
$397$	10.4828	−	18.1567i	0.526115	−	0.911258i	−0.473422	−	0.880836i	$-0.656981\pi$
$397$	10.4828	−	18.1567i	0.526115	−	0.911258i	0.999537	−	0.0304226i	$-0.00968532\pi$
$398$	−6.47738			−0.324682
$399$	5.60776	+	21.2005i	0.280739	+	1.06135i
$400$	−8.96422			−0.448211
$401$	20.3964	+	11.7758i	1.01855	+	0.588057i	0.913682	−	0.406429i	$-0.133226\pi$
$401$	20.3964	+	11.7758i	1.01855	+	0.588057i	0.104863	+	0.994487i	$0.466560\pi$
$402$	−0.611702	+	1.20609i	−0.0305089	+	0.0601541i
$403$	−10.1731	+	5.87347i	−0.506761	+	0.292578i
$404$	−0.661912	+	1.14646i	−0.0329313	+	0.0570387i
$405$	−24.8248	+	22.6899i	−1.23355	+	1.12747i
$406$	13.6229	+	15.2851i	0.676095	+	0.758586i
$407$	4.15737	+	7.51035i	0.206073	+	0.372274i
$408$	1.59394	−	0.0865151i	0.0789117	−	0.00428314i
$409$	10.2853	−	5.93820i	0.508573	−	0.293625i	−0.223674	−	0.974664i	$-0.571805\pi$
$409$	10.2853	−	5.93820i	0.508573	−	0.293625i	0.732247	+	0.681039i	$0.238472\pi$
$410$	−13.2834	+	7.66918i	−0.656021	+	0.378754i
$411$	−1.21330	−	22.3535i	−0.0598475	−	1.10262i
$412$	9.89908			0.487693
$413$	4.74716	+	22.9046i	0.233593	+	1.12706i
$414$	−15.6734	−	6.90831i	−0.770303	−	0.339525i
$415$	41.0301	+	23.6887i	2.01409	+	1.16283i
$416$	4.01896	−	2.32035i	0.197046	−	0.113764i
$417$	−12.4946	−	6.33701i	−0.611865	−	0.310325i
$418$	0.286196	−	15.8689i	0.0139983	−	0.776172i
$419$		−	21.5571i		−	1.05313i	−0.850134	−	0.526567i	$-0.823479\pi$
$419$		−	21.5571i		−	1.05313i	0.850134	−	0.526567i	$-0.176521\pi$
$420$	−12.1477	+	12.0699i	−0.592745	+	0.588952i
$421$	−12.1688			−0.593070			−0.296535	−	0.955022i	$-0.595831\pi$
$421$	−12.1688			−0.593070			−0.296535	+	0.955022i	$0.595831\pi$
$422$	15.4275	+	8.90708i	0.751000	+	0.433590i
$423$	−1.86028	−	17.0862i	−0.0904499	−	0.830760i
$424$	3.30063	−	1.90562i	0.160293	−	0.0925452i
$425$	−4.13078	+	7.15472i	−0.200372	+	0.347055i
$426$	−16.6817	+	10.8775i	−0.808232	+	0.527017i
$427$	14.8871	−	13.2682i	0.720438	−	0.642095i
$428$	11.2337			0.543000
$429$	22.5898	−	14.1560i	1.09064	−	0.683460i
$430$	4.10460	+	7.10937i	0.197941	+	0.342844i
$431$	6.76221	+	11.7125i	0.325724	+	0.564171i	0.981659	−	0.190647i	$-0.0610585\pi$
$431$	6.76221	+	11.7125i	0.325724	+	0.564171i	−0.655934	+	0.754818i	$0.727725\pi$
$432$	1.83497	−	4.86137i	0.0882851	−	0.233893i
$433$	34.3316			1.64987			0.824937	−	0.565225i	$-0.191211\pi$
$433$	34.3316			1.64987			0.824937	+	0.565225i	$0.191211\pi$
$434$	−2.10183	+	6.35879i	−0.100891	+	0.305232i
$435$	41.9570	−	27.3585i	2.01168	−	1.31174i
$436$	3.95986	+	2.28623i	0.189643	+	0.109490i
$437$	13.6610	+	23.6616i	0.653496	+	1.13189i
$438$	−16.6857	−	8.46266i	−0.797275	−	0.404361i
$439$	−2.95877	−	1.70824i	−0.141214	−	0.0815301i	0.427728	−	0.903907i	$-0.359314\pi$
$439$	−2.95877	−	1.70824i	−0.141214	−	0.0815301i	−0.568943	+	0.822377i	$0.692647\pi$
$440$	10.8433	−	6.00235i	0.516936	−	0.286151i
$441$	−0.134832	+	20.9996i	−0.00642057	+	0.999979i
$442$		−	4.27694i		−	0.203433i
$443$	21.5391	+	12.4356i	1.02336	+	0.590835i	0.915074	−	0.403286i	$-0.132132\pi$
$443$	21.5391	+	12.4356i	1.02336	+	0.590835i	0.108281	+	0.994120i	$0.465465\pi$
$444$	2.02778	−	3.99814i	0.0962340	−	0.189744i
$445$	−16.0727	−	27.8388i	−0.761921	−	1.31969i
$446$	−4.55482	+	7.88917i	−0.215677	+	0.373563i
$447$	−12.4891	−	19.1532i	−0.590714	−	0.905918i
$448$	0.830341	−	2.51208i	0.0392299	−	0.118685i
$449$			12.2457i			0.577908i	0.957343	+	0.288954i	$0.0933075\pi$
$449$			12.2457i			0.577908i	−0.957343	+	0.288954i	$0.906693\pi$
$450$	15.8881	+	21.6975i	0.748974	+	1.02283i
$451$	7.01819	−	11.6649i	0.330474	−	0.549279i
$452$	−6.51444	+	3.76112i	−0.306414	+	0.176908i
$453$	1.11791	+	20.5961i	0.0525240	+	0.967691i
$454$	−25.0737			−1.17677
$455$	30.5275	+	34.2522i	1.43115	+	1.60577i
$456$	−6.94298	+	4.52725i	−0.325135	+	0.212008i
$457$	26.7154	+	15.4241i	1.24969	+	0.721511i	0.971048	−	0.238883i	$-0.0767814\pi$
$457$	26.7154	+	15.4241i	1.24969	+	0.721511i	0.278645	+	0.960394i	$0.410115\pi$
$458$	11.5525	+	20.0095i	0.539811	+	0.934980i
$459$	−3.03449	−	3.70472i	−0.141638	−	0.172922i
$460$	−10.6677	+	18.4770i	−0.497385	+	0.861496i
$461$	−3.40330			−0.158507			−0.0792537	−	0.996854i	$-0.525254\pi$
$461$	−3.40330			−0.158507			−0.0792537	+	0.996854i	$0.525254\pi$
$462$	4.24467	−	14.5939i	0.197480	−	0.678971i
$463$	−15.8266			−0.735522			−0.367761	−	0.929920i	$-0.619876\pi$
$463$	−15.8266			−0.735522			−0.367761	+	0.929920i	$0.619876\pi$
$464$	−3.86938	+	6.70196i	−0.179631	+	0.311130i
$465$	14.6118	+	7.41079i	0.677605	+	0.343667i
$466$	−11.6393	−	20.1599i	−0.539181	−	0.933889i
$467$	18.9467	+	10.9389i	0.876750	+	0.506192i	0.869586	−	0.493782i	$-0.164386\pi$
$467$	18.9467	+	10.9389i	0.876750	+	0.506192i	0.00716472	+	0.999974i	$0.497719\pi$
$468$	−12.7395	−	5.61516i	−0.588883	−	0.259561i
$469$	2.02275	−	0.419231i	0.0934017	−	0.0193583i
$470$	−21.4088			−0.987514
$471$	20.9265	−	1.13584i	0.964240	−	0.0523367i
$472$	−7.65662	+	4.42055i	−0.352424	+	0.203472i
$473$	−6.24314	−	3.75618i	−0.287060	−	0.172709i
$474$	−1.61613	−	29.7752i	−0.0742313	−	1.36762i
$475$		−	42.8976i		−	1.96828i
$476$	−1.62237	−	1.82031i	−0.0743611	−	0.0834340i
$477$	−10.4625	−	4.61153i	−0.479045	−	0.211148i
$478$	1.47636	−	2.55714i	0.0675273	−	0.116961i
$479$	−12.2718	−	21.2553i	−0.560711	−	0.971180i	−0.997435	−	0.0715839i	$-0.977195\pi$
$479$	−12.2718	−	21.2553i	−0.560711	−	0.971180i	0.436724	−	0.899596i	$-0.356139\pi$
$480$	−5.77247	−	2.92767i	−0.263476	−	0.133629i
$481$	−10.4021	−	6.00563i	−0.474293	−	0.273833i
$482$			3.67675i			0.167471i
$483$	6.69055	+	25.2940i	0.304431	+	1.15092i
$484$	−5.83993	+	9.32176i	−0.265451	+	0.423717i
$485$	−39.3796	−	22.7358i	−1.78814	−	1.03238i
$486$	−15.0190	+	4.17479i	−0.681277	+	0.189372i
$487$	−18.0891	−	31.3313i	−0.819697	−	1.41976i	−0.905905	−	0.423480i	$-0.860808\pi$
$487$	−18.0891	−	31.3313i	−0.819697	−	1.41976i	0.0862081	−	0.996277i	$-0.472525\pi$
$488$	6.52747	+	3.76863i	0.295484	+	0.170598i
$489$	−1.45771	−	2.23553i	−0.0659197	−	0.101094i
$490$	25.9857	+	2.99816i	1.17392	+	0.135443i
$491$	−39.6660			−1.79010			−0.895050	−	0.445965i	$-0.852861\pi$
$491$	−39.6660			−1.79010			−0.895050	+	0.445965i	$0.852861\pi$
$492$	−7.09892	+	0.385313i	−0.320044	+	0.0173712i
$493$	3.56607	+	6.17662i	0.160608	+	0.278181i
$494$	11.1039	+	19.2324i	0.499586	+	0.865309i
$495$	−33.7471	−	15.6073i	−1.51682	−	0.701498i
$496$	−2.53129			−0.113658
$497$	28.8834	+	9.54712i	1.29560	+	0.428247i
$498$	11.9944	+	18.3945i	0.537480	+	0.824278i
$499$	−16.0605	+	27.8176i	−0.718966	+	1.24529i	0.242444	+	0.970165i	$0.422051\pi$
$499$	−16.0605	+	27.8176i	−0.718966	+	1.24529i	−0.961410	+	0.275120i	$0.911282\pi$
$500$	12.8291	−	7.40689i	0.573736	−	0.331246i
$501$	8.00747	−	15.7883i	0.357747	−	0.705367i
$502$	23.4533	+	13.5408i	1.04677	+	0.604353i
$503$	8.24994			0.367847			0.183923	−	0.982941i	$-0.441120\pi$
$503$	8.24994			0.367847			0.183923	+	0.982941i	$0.441120\pi$
$504$	−7.55207	+	2.44259i	−0.336396	+	0.108801i
$505$		−	4.94696i		−	0.220137i
$506$	0.341458	−	18.9330i	0.0151796	−	0.841673i
$507$	−6.68763	+	13.1859i	−0.297008	+	0.585608i
$508$	4.45890	−	2.57435i	0.197832	−	0.114218i
$509$	3.24742	+	1.87490i	0.143939	+	0.0831033i	0.570240	−	0.821478i	$-0.306850\pi$
$509$	3.24742	+	1.87490i	0.143939	+	0.0831033i	−0.426301	+	0.904581i	$0.640184\pi$
$510$	−4.99670	+	3.25815i	−0.221257	+	0.144273i
$511$	5.79989	+	27.9839i	0.256572	+	1.23793i
$512$	1.00000			0.0441942
$513$	23.2637	+	8.78112i	1.02712	+	0.387696i
$514$	12.5519	−	7.24684i	0.553640	−	0.319644i
$515$	−32.0357	+	18.4958i	−1.41166	+	0.815022i
$516$	0.206222	+	3.79939i	0.00907841	+	0.167259i
$517$	16.6241	−	9.20231i	0.731128	−	0.404717i
$518$	−6.70535	+	1.38974i	−0.294616	+	0.0610616i
$519$	−6.61782	−	10.1491i	−0.290490	−	0.445495i
$520$	−8.67085	+	15.0184i	−0.380242	+	0.658598i
$521$	20.4859	−	11.8275i	0.897504	−	0.518174i	0.0211142	−	0.999777i	$-0.493279\pi$
$521$	20.4859	−	11.8275i	0.897504	−	0.518174i	0.876389	+	0.481603i	$0.159945\pi$
$522$	23.0799	−	2.51284i	1.01018	−	0.109984i
$523$	−16.3582	−	9.44443i	−0.715295	−	0.412976i	0.0977232	−	0.995214i	$-0.468844\pi$
$523$	−16.3582	−	9.44443i	−0.715295	−	0.412976i	−0.813019	+	0.582238i	$0.802177\pi$
$524$	15.8256			0.691343
$525$	10.7594	−	39.6451i	0.469579	−	1.73026i
$526$	14.5018			0.632306
$527$	−1.16644	+	2.02033i	−0.0508108	+	0.0880068i
$528$	5.74080	−	0.207858i	0.249836	−	0.00904585i
$529$	4.79882	+	8.31181i	0.208645	+	0.361383i
$530$	−7.12107	+	12.3341i	−0.309319	+	0.535757i
$531$	24.2703	+	10.6976i	1.05324	+	0.464235i
$532$	12.0214	+	3.97354i	0.521192	+	0.172275i
$533$			19.0482i			0.825069i
$534$	−0.807522	−	14.8776i	−0.0349449	−	0.643818i
$535$	−36.3547	+	20.9894i	−1.57175	+	0.907451i
$536$	0.390387	+	0.676170i	0.0168622	+	0.0292061i
$537$	2.17553	+	40.0816i	0.0938812	+	1.72965i
$538$			7.69686i			0.331835i
$539$	−21.4669	+	8.84154i	−0.924644	+	0.380832i
$540$	3.14477	+	19.1610i	0.135329	+	0.824559i
$541$	−30.8245	−	17.7966i	−1.32525	−	0.765134i	−0.340690	−	0.940176i	$-0.610661\pi$
$541$	−30.8245	−	17.7966i	−1.32525	−	0.765134i	−0.984561	+	0.175042i	$0.943994\pi$
$542$	−2.86928	+	1.65658i	−0.123246	+	0.0711561i
$543$	−4.96823	+	9.79580i	−0.213207	+	0.420378i
$544$	0.460807	−	0.798142i	0.0197570	−	0.0342201i
$545$	−17.0867			−0.731913
$546$	5.43816	+	20.5593i	0.232732	+	0.879856i
$547$			31.2280i			1.33521i	0.744514	+	0.667607i	$0.232681\pi$
$547$			31.2280i			1.33521i	−0.744514	+	0.667607i	$0.767319\pi$
$548$	−11.1932	−	6.46241i	−0.478151	−	0.276061i
$549$	−2.44742	−	22.4790i	−0.104453	−	0.959379i
$550$	−15.3273	+	25.4755i	−0.653560	+	1.08628i
$551$	−32.0717	−	18.5166i	−1.36630	−	0.788834i
$552$	−8.28358	+	5.40141i	−0.352573	+	0.229899i
$553$	−34.0040	+	30.3063i	−1.44600	+	1.28876i
$554$		−	8.95881i		−	0.380623i
$555$	0.907938	+	16.7277i	0.0385398	+	0.710050i
$556$	−7.00488	+	4.04427i	−0.297073	+	0.171515i
$557$	−7.73600	−	13.3991i	−0.327785	−	0.567740i	0.654287	−	0.756246i	$-0.272969\pi$
$557$	−7.73600	−	13.3991i	−0.327785	−	0.567740i	−0.982072	+	0.188506i	$0.939635\pi$
$558$	4.48644	+	6.12688i	0.189926	+	0.259371i
$559$	10.1947			0.431191
$560$	2.00648	+	9.68109i	0.0847895	+	0.409101i
$561$	2.47950	−	4.67776i	0.104685	−	0.197495i
$562$	−11.4738	+	19.8733i	−0.483994	+	0.838303i
$563$	0.771946	+	1.33705i	0.0325336	+	0.0563499i	0.881834	−	0.471560i	$-0.156309\pi$
$563$	0.771946	+	1.33705i	0.0325336	+	0.0563499i	−0.849300	+	0.527910i	$0.822976\pi$
$564$	−8.84987	−	4.48847i	−0.372647	−	0.188999i
$565$	14.0548	−	24.3436i	0.591290	−	1.02414i
$566$			25.9431i			1.09047i
$567$	19.2974	+	13.9503i	0.810416	+	0.585855i
$568$			11.4978i			0.482438i
$569$	11.5873	−	20.0697i	0.485763	−	0.841366i	−0.514103	−	0.857728i	$-0.671875\pi$
$569$	11.5873	−	20.0697i	0.485763	−	0.841366i	0.999866	+	0.0163623i	$0.00520852\pi$
$570$	14.0102	−	27.6237i	0.586822	−	1.15703i
$571$	−7.03226	+	4.06008i	−0.294291	+	0.169909i	−0.639875	−	0.768479i	$-0.721014\pi$
$571$	−7.03226	+	4.06008i	−0.294291	+	0.169909i	0.345584	+	0.938388i	$0.387681\pi$
$572$	0.277541	−	15.3889i	0.0116046	−	0.643444i
$573$	10.2007	−	6.65151i	0.426142	−	0.277871i
$574$	7.22554	+	8.10714i	0.301588	+	0.338385i
$575$		−	51.1806i		−	2.13438i
$576$	−1.77239	−	2.42046i	−0.0738498	−	0.100852i
$577$	22.9056	+	39.6736i	0.953571	+	1.65163i	0.737605	+	0.675232i	$0.235957\pi$
$577$	22.9056	+	39.6736i	0.953571	+	1.65163i	0.215965	+	0.976401i	$0.430710\pi$
$578$	8.07531	+	13.9869i	0.335889	+	0.581776i
$579$	0.818201	+	15.0744i	0.0340033	+	0.626469i
$580$		−	28.9187i		−	1.20079i
$581$	10.5274	−	31.8491i	0.436749	−	1.32132i
$582$	−11.5119	−	17.6546i	−0.477183	−	0.731807i
$583$	0.227935	−	12.6384i	0.00944009	−	0.523429i
$584$	−9.35455	+	5.40085i	−0.387094	+	0.223489i
$585$	51.7195	−	5.63101i	2.13834	−	0.232813i
$586$	2.78352	−	4.82120i	0.114986	−	0.199162i
$587$		−	8.71794i		−	0.359828i	−0.983682	−	0.179914i	$-0.942418\pi$
$587$		−	8.71794i		−	0.359828i	0.983682	−	0.179914i	$-0.0575820\pi$
$588$	10.1133	+	6.68742i	0.417065	+	0.275784i
$589$		−	12.1133i		−	0.499119i
$590$	16.5190	−	28.6118i	0.680078	−	1.17793i
$591$	0.436200	−	0.860050i	0.0179429	−	0.0353777i
$592$	−1.29412	−	2.24149i	−0.0531881	−	0.0921245i
$593$	11.1048	−	19.2340i	0.456019	−	0.789848i	−0.542727	−	0.839909i	$-0.682608\pi$
$593$	11.1048	−	19.2340i	0.456019	−	0.789848i	0.998746	+	0.0500613i	$0.0159417\pi$
$594$	−10.6781	−	13.5270i	−0.438127	−	0.555018i
$595$	8.65149	+	2.85966i	0.354676	+	0.117235i
$596$	−13.2013			−0.540747
$597$	11.2027	−	0.608054i	0.458495	−	0.0248860i
$598$	13.2479	+	22.9460i	0.541746	+	0.938332i
$599$	−6.10885	+	3.52694i	−0.249601	+	0.144107i	−0.619581	−	0.784932i	$-0.712698\pi$
$599$	−6.10885	+	3.52694i	−0.249601	+	0.144107i	0.369981	+	0.929039i	$0.379364\pi$
$600$	15.5037	−	0.841502i	0.632934	−	0.0343542i
$601$		−	19.4191i		−	0.792122i	−0.918224	−	0.396061i	$-0.870377\pi$
$601$		−	19.4191i		−	0.792122i	0.918224	−	0.396061i	$-0.129623\pi$
$602$	4.33899	−	3.86716i	0.176844	−	0.157614i
$603$	0.944722	−	2.14336i	0.0384721	−	0.0872842i
$604$	10.3132	+	5.95435i	0.419639	+	0.242279i
$605$	1.48220	−	41.0789i	0.0602601	−	1.67009i
$606$	1.03716	−	2.04495i	0.0421316	−	0.0830705i
$607$	17.1496	+	9.90133i	0.696081	+	0.401882i	0.805886	−	0.592071i	$-0.201689\pi$
$607$	17.1496	+	9.90133i	0.696081	+	0.401882i	−0.109805	+	0.993953i	$0.535023\pi$
$608$			4.78543i			0.194075i
$609$	−24.9958	−	25.1568i	−1.01288	−	1.01940i
$610$	−28.1658			−1.14040
$611$	−13.2934	+	23.0249i	−0.537794	+	0.931487i
$612$	−2.74860	+	0.299257i	−0.111106	+	0.0120967i
$613$	−41.1230	+	23.7424i	−1.66094	+	0.958945i	−0.688675	+	0.725070i	$0.741807\pi$
$613$	−41.1230	+	23.7424i	−1.66094	+	0.958945i	−0.972267	+	0.233875i	$0.924859\pi$
$614$	−26.1600	−	15.1035i	−1.05573	−	0.609526i
$615$	22.2538	−	14.5108i	0.897359	−	0.585134i
$616$	−5.71935	−	6.65500i	−0.230439	−	0.268137i
$617$		−	38.1302i		−	1.53506i	−0.641011	−	0.767532i	$-0.721485\pi$
$617$		−	38.1302i		−	1.53506i	0.641011	−	0.767532i	$-0.278515\pi$
$618$	−17.1205	+	0.929260i	−0.688688	+	0.0373803i
$619$	−23.0035	−	39.8432i	−0.924588	−	1.60143i	−0.792222	−	0.610233i	$-0.791076\pi$
$619$	−23.0035	−	39.8432i	−0.924588	−	1.60143i	−0.132366	−	0.991201i	$-0.542257\pi$
$620$	8.19182	−	4.72955i	0.328991	−	0.189943i
$621$	27.7557	+	10.4766i	1.11380	+	0.420413i
$622$		−	0.915784i		−	0.0367196i
$623$	−16.9906	+	15.1430i	−0.680714	+	0.606691i
$624$	−6.73300	+	4.39033i	−0.269536	+	0.175754i
$625$	−5.26807	+	9.12457i	−0.210723	+	0.364983i
$626$	2.87594	+	4.98127i	0.114946	+	0.199092i
$627$	0.994688	+	27.4722i	0.0397240	+	1.09713i
$628$	6.04984	−	10.4786i	0.241415	−	0.418143i
$629$	−2.38536			−0.0951107
$630$	19.8764	−	22.0153i	0.791895	−	0.877112i
$631$	30.5055			1.21441			0.607203	−	0.794547i	$-0.292292\pi$
$631$	30.5055			1.21441			0.607203	+	0.794547i	$0.292292\pi$
$632$	−14.9095	−	8.60802i	−0.593069	−	0.342409i
$633$	−27.5181	−	13.9566i	−1.09375	−	0.554725i
$634$	9.09364	−	5.25022i	0.361155	−	0.208513i
$635$	−9.62002	+	16.6624i	−0.381759	+	0.661226i
$636$	−5.52958	+	3.60562i	−0.219262	+	0.142972i
$637$	19.3599	−	26.0857i	0.767067	−	1.03355i
$638$	12.4304	+	22.4557i	0.492123	+	0.889028i
$639$	27.8300	−	20.3787i	1.10094	−	0.806169i
$640$	−3.23623	+	1.86844i	−0.127923	+	0.0738564i
$641$	−10.5012	+	6.06289i	−0.414774	+	0.239470i	−0.692839	−	0.721092i	$-0.743640\pi$
$641$	−10.5012	+	6.06289i	−0.414774	+	0.239470i	0.278065	+	0.960562i	$0.410307\pi$
$642$	−19.4287	+	1.05454i	−0.766790	+	0.0416195i
$643$	11.5883			0.456999			0.228499	−	0.973544i	$-0.426618\pi$
$643$	11.5883			0.456999			0.228499	+	0.973544i	$0.426618\pi$
$644$	14.3425	+	4.74078i	0.565175	+	0.186813i
$645$	−7.76630	−	11.9104i	−0.305798	−	0.468971i
$646$	3.81945	+	2.20516i	0.150274	+	0.0867609i
$647$	17.3213	−	10.0004i	0.680969	−	0.393158i	−0.119251	−	0.992864i	$-0.538049\pi$
$647$	17.3213	−	10.0004i	0.680969	−	0.393158i	0.800220	+	0.599707i	$0.204716\pi$
$648$	−2.71724	+	8.58001i	−0.106743	+	0.337055i
$649$	−0.528749	+	29.3178i	−0.0207552	+	1.15083i
$650$		−	41.6002i		−	1.63170i
$651$	3.03821	−	11.1949i	0.119077	−	0.438761i
$652$	−1.54083			−0.0603437
$653$	18.1507	+	10.4793i	0.710291	+	0.410087i	0.811169	−	0.584812i	$-0.198832\pi$
$653$	18.1507	+	10.4793i	0.710291	+	0.410087i	−0.100878	+	0.994899i	$0.532165\pi$
$654$	−7.06322	−	3.58232i	−0.276194	−	0.140080i
$655$	−51.2151	+	29.5691i	−2.00114	+	1.15536i
$656$	−2.05230	+	3.55469i	−0.0801288	+	0.138787i
$657$	29.6525	+	13.0699i	1.15685	+	0.509904i
$658$	3.07618	+	14.8422i	0.119922	+	0.578611i
$659$	−8.15565			−0.317699			−0.158850	−	0.987303i	$-0.550778\pi$
$659$	−8.15565			−0.317699			−0.158850	+	0.987303i	$0.550778\pi$
$660$	−18.1902	+	11.3990i	−0.708051	+	0.443705i
$661$	−17.6023	−	30.4881i	−0.684650	−	1.18585i	−0.973547	−	0.228489i	$-0.926622\pi$
$661$	−17.6023	−	30.4881i	−0.684650	−	1.18585i	0.288896	−	0.957360i	$-0.406712\pi$
$662$	7.54164	+	13.0625i	0.293114	+	0.507689i
$663$	0.401491	+	7.39698i	0.0155926	+	0.287275i
$664$	12.6784			0.492016
$665$	−46.3282	+	9.60189i	−1.79653	+	0.372345i
$666$	−3.13173	+	7.10517i	−0.121352	+	0.275320i
$667$	−38.2644	−	22.0919i	−1.48160	−	0.855404i
$668$	−5.11035	−	8.85139i	−0.197726	−	0.342471i
$669$	7.13699	−	14.0719i	0.275932	−	0.544053i
$670$	−2.52676	−	1.45883i	−0.0976173	−	0.0563594i
$671$	21.8710	−	12.1067i	0.844321	−	0.467375i
$672$	−1.20026	+	4.42260i	−0.0463011	+	0.170605i
$673$			20.2008i			0.778685i	0.921093	+	0.389342i	$0.127298\pi$
$673$			20.2008i			0.778685i	−0.921093	+	0.389342i	$0.872702\pi$
$674$	12.8492	+	7.41850i	0.494933	+	0.285750i
$675$	−29.5154	−	36.0345i	−1.13605	−	1.38697i
$676$	4.26804	+	7.39246i	0.164155	+	0.284325i
$677$	0.814387	−	1.41056i	0.0312995	−	0.0542122i	−0.849951	−	0.526861i	$-0.823369\pi$
$677$	0.814387	−	1.41056i	0.0312995	−	0.0542122i	0.881251	+	0.472649i	$0.156702\pi$
$678$	10.9137	−	7.11640i	0.419138	−	0.273304i
$679$	−10.1039	+	30.5679i	−0.387752	+	1.17309i
$680$			3.44396i			0.132070i
$681$	43.3651	−	2.35376i	1.66176	−	0.0901961i
$682$	−4.32809	+	7.19369i	−0.165731	+	0.275461i
$683$	26.5384	−	15.3220i	1.01546	−	0.586278i	0.102677	−	0.994715i	$-0.467259\pi$
$683$	26.5384	−	15.3220i	1.01546	−	0.586278i	0.912787	+	0.408436i	$0.133926\pi$
$684$	11.5829	−	8.48166i	0.442884	−	0.324304i
$685$	48.2984			1.84539
$686$	−1.65526	−	18.4461i	−0.0631982	−	0.704277i
$687$	−21.8584	−	33.5220i	−0.833950	−	1.27894i
$688$	1.90249	+	1.09840i	0.0725318	+	0.0418763i
$689$	8.84341	+	15.3172i	0.336907	+	0.583540i
$690$	16.7154	−	32.9575i	0.636343	−	1.25467i
$691$	−0.398760	+	0.690673i	−0.0151696	+	0.0262744i	−0.873511	−	0.486805i	$-0.838162\pi$
$691$	−0.398760	+	0.690673i	−0.0151696	+	0.0262744i	0.858341	+	0.513080i	$0.171495\pi$
$692$	−6.99522			−0.265918
$693$	−5.97119	+	25.6387i	−0.226827	+	0.973935i
$694$	−1.69957			−0.0645148
$695$	15.1129	−	26.1764i	0.573266	−	0.992926i
$696$	6.06297	−	11.9543i	0.229816	−	0.453126i
$697$	1.89143	+	3.27605i	0.0716430	+	0.124089i
$698$	17.4664	+	10.0842i	0.661112	+	0.381693i
$699$	22.0227	+	33.7740i	0.832976	+	1.27745i
$700$	−15.7802	−	17.7055i	−0.596435	−	0.669207i
$701$	31.8559			1.20318			0.601591	−	0.798804i	$-0.294534\pi$
$701$	31.8559			1.20318			0.601591	+	0.798804i	$0.294534\pi$
$702$	22.5601	+	8.51554i	0.851477	+	0.321398i
$703$	10.7265	−	6.19293i	0.404556	−	0.233571i
$704$	1.70984	−	2.84191i	0.0644419	−	0.107109i
$705$	37.0266	−	2.00972i	1.39450	−	0.0756903i
$706$		−	11.4189i		−	0.429755i
$707$	−3.42962	+	0.710817i	−0.128984	+	0.0267330i
$708$	12.8272	−	8.36412i	0.482075	−	0.314343i
$709$	−15.7500	+	27.2797i	−0.591502	+	1.02451i	0.402528	+	0.915408i	$0.368132\pi$
$709$	−15.7500	+	27.2797i	−0.591502	+	1.02451i	−0.994030	+	0.109104i	$0.965202\pi$
$710$	−21.4830	−	37.2096i	−0.806241	−	1.39645i
$711$	5.59021	+	51.3447i	0.209649	+	1.92558i
$712$	−7.44976	−	4.30112i	−0.279192	−	0.161191i
$713$		−	14.4522i		−	0.541240i
$714$	2.97677	+	2.99595i	0.111403	+	0.112120i
$715$	27.8551	+	50.3207i	1.04172	+	1.88189i
$716$	20.0703	+	11.5876i	0.750062	+	0.433049i
$717$	−2.31333	+	4.56118i	−0.0863930	+	0.170340i
$718$	4.22498	+	7.31788i	0.157675	+	0.273101i
$719$	−6.04825	−	3.49196i	−0.225562	−	0.130228i	0.382961	−	0.923764i	$-0.374904\pi$
$719$	−6.04825	−	3.49196i	−0.225562	−	0.130228i	−0.608523	+	0.793536i	$0.708238\pi$
$720$	10.2583	+	4.52155i	0.382306	+	0.168508i
$721$	17.4259	+	19.5520i	0.648973	+	0.728155i
$722$	−3.90031			−0.145154
$723$	−0.345149	−	6.35896i	−0.0128362	−	0.236492i
$724$	3.17071	+	5.49183i	0.117839	+	0.204102i
$725$	34.6859	+	60.0778i	1.28820	+	2.23123i
$726$	9.22512	−	16.6703i	0.342376	−	0.618691i
$727$	−33.1623			−1.22992			−0.614960	−	0.788558i	$-0.710828\pi$
$727$	−33.1623			−1.22992			−0.614960	+	0.788558i	$0.710828\pi$
$728$	11.6578	+	3.85336i	0.432067	+	0.142815i
$729$	25.5836	−	8.63020i	0.947540	−	0.319637i
$730$	20.1823	−	34.9568i	0.746980	−	1.29381i
$731$	1.75336	−	1.01231i	0.0648505	−	0.0374415i
$732$	−11.6431	−	5.90512i	−0.430340	−	0.218259i
$733$	21.5001	+	12.4131i	0.794123	+	0.458487i	0.841412	−	0.540394i	$-0.181725\pi$
$733$	21.5001	+	12.4131i	0.794123	+	0.458487i	−0.0472893	+	0.998881i	$0.515058\pi$
$734$	0.312061			0.0115184
$735$	−45.2239	−	2.74597i	−1.66811	−	0.101287i
$736$			5.70943i			0.210453i
$737$	2.58911	+	0.0466948i	0.0953712	+	0.00172003i
$738$	12.2415	−	1.33280i	0.450614	−	0.0490611i
$739$	1.10754	−	0.639441i	0.0407417	−	0.0235222i	−0.479491	−	0.877547i	$-0.659179\pi$
$739$	1.10754	−	0.639441i	0.0407417	−	0.0235222i	0.520233	+	0.854025i	$0.325845\pi$
$740$	8.37615	+	4.83597i	0.307913	+	0.177774i
$741$	−21.0096	−	32.2203i	−0.771807	−	1.18364i
$742$	9.57414	+	3.16463i	0.351478	+	0.116177i
$743$	−0.935605			−0.0343240			−0.0171620	−	0.999853i	$-0.505463\pi$
$743$	−0.935605			−0.0343240			−0.0171620	+	0.999853i	$0.505463\pi$
$744$	4.37787	−	0.237621i	0.160501	−	0.00871159i
$745$	42.7225	−	24.6658i	1.56523	−	0.903686i
$746$	29.1559	−	16.8331i	1.06747	−	0.616305i
$747$	−22.4711	−	30.6875i	−0.822173	−	1.12280i
$748$	−1.48034	−	2.67427i	−0.0541267	−	0.0977808i
$749$	19.7752	+	22.1880i	0.722571	+	0.810733i
$750$	−21.4927	+	14.0146i	−0.784803	+	0.511740i
$751$	−3.90274	+	6.75974i	−0.142413	+	0.246666i	−0.928405	−	0.371570i	$-0.878819\pi$
$751$	−3.90274	+	6.75974i	−0.142413	+	0.246666i	0.785992	+	0.618237i	$0.212153\pi$
$752$	−4.96151	+	2.86453i	−0.180928	+	0.104459i
$753$	−41.8337	−	21.2172i	−1.52450	−	0.773196i
$754$	−31.1017	−	17.9566i	−1.13266	−	0.653941i
$755$	−44.5013			−1.61957
$756$	12.8321	−	4.93340i	0.466697	−	0.179426i
$757$	48.4080			1.75942			0.879710	−	0.475510i	$-0.157737\pi$
$757$	48.4080			1.75942			0.879710	+	0.475510i	$0.157737\pi$
$758$	−4.48621	+	7.77035i	−0.162947	+	0.282232i
$759$	1.18675	+	32.7767i	0.0430763	+	1.18972i
$760$	−8.94127	−	15.4867i	−0.324334	−	0.561763i
$761$	−25.7356	+	44.5754i	−0.932915	+	1.61586i	−0.154604	+	0.987977i	$0.549410\pi$
$761$	−25.7356	+	44.5754i	−0.932915	+	1.61586i	−0.778311	+	0.627879i	$0.783923\pi$
$762$	−7.47004	+	4.87092i	−0.270611	+	0.176455i
$763$	2.45515	+	11.8458i	0.0888822	+	0.428848i
$764$		−	7.03083i		−	0.254366i
$765$	8.33596	−	6.10405i	0.301387	−	0.220692i
$766$	−6.48945	+	3.74669i	−0.234473	+	0.135373i
$767$	−20.5144	−	35.5320i	−0.740733	−	1.28299i
$768$	−1.72951	+	0.0938734i	−0.0624081	+	0.00338737i
$769$			2.65444i			0.0957217i	0.998854	+	0.0478609i	$0.0152404\pi$
$769$			2.65444i			0.0957217i	−0.998854	+	0.0478609i	$0.984760\pi$
$770$	30.9436	+	10.8508i	1.11513	+	0.391037i
$771$	−21.0283	+	13.7117i	−0.757315	+	0.493816i
$772$	7.54828	+	4.35800i	0.271668	+	0.156848i
$773$	19.4199	−	11.2121i	0.698487	−	0.403272i	−0.108297	−	0.994119i	$-0.534540\pi$
$773$	19.4199	−	11.2121i	0.698487	−	0.403272i	0.806784	+	0.590847i	$0.201206\pi$
$774$	−0.713324	−	6.55171i	−0.0256399	−	0.235496i
$775$	−11.3455	+	19.6510i	−0.407543	+	0.705885i
$776$	−12.1684			−0.436819
$777$	11.4665	−	3.03301i	0.411358	−	0.108809i
$778$		−	11.5171i		−	0.412906i
$779$	−17.0107	−	9.82112i	−0.609471	−	0.351878i
$780$	13.5865	−	26.7883i	0.486473	−	0.959174i
$781$	32.6758	+	19.6594i	1.16923	+	0.703469i
$782$	4.55694	+	2.63095i	0.162956	+	0.0940826i
$783$	−39.6809	+	6.51256i	−1.41808	+	0.232740i
$784$	6.42339	−	2.78211i	0.229407	−	0.0993609i
$785$			45.2150i			1.61379i
$786$	−27.3704	+	1.48560i	−0.976270	+	0.0529896i
$787$	15.3260	−	8.84845i	0.546312	−	0.315413i	−0.201321	−	0.979525i	$-0.564524\pi$
$787$	15.3260	−	8.84845i	0.546312	−	0.315413i	0.747633	+	0.664112i	$0.231190\pi$
$788$	−0.278382	−	0.482171i	−0.00991694	−	0.0171766i
$789$	−25.0809	+	1.36133i	−0.892902	+	0.0484646i
$790$	64.3342			2.28891
$791$	−18.8964	−	6.24602i	−0.671880	−	0.222083i
$792$	−9.90923	+	0.898400i	−0.352109	+	0.0319232i
$793$	−17.4891	+	30.2920i	−0.621056	+	1.07570i
$794$	10.4828	+	18.1567i	0.372020	+	0.644357i
$795$	11.1581	−	22.0003i	0.395736	−	0.780270i
$796$	3.23869	−	5.60958i	0.114792	−	0.198826i
$797$		−	28.8638i		−	1.02241i	−0.859459	−	0.511205i	$-0.829199\pi$
$797$		−	28.8638i		−	1.02241i	0.859459	−	0.511205i	$-0.170801\pi$
$798$	−21.1640	−	5.74377i	−0.749198	−	0.203327i
$799$			5.27999i			0.186793i
$800$	4.48211	−	7.76324i	0.158467	−	0.274472i
$801$	2.79323	+	25.6551i	0.0986938	+	0.906479i
$802$	−20.3964	+	11.7758i	−0.720220	+	0.415819i
$803$	−0.646005	+	35.8194i	−0.0227970	+	1.26404i
$804$	−0.738651	−	1.13279i	−0.0260502	−	0.0399505i
$805$	−55.2736	+	11.4559i	−1.94814	+	0.403767i
$806$		−	11.7469i		−	0.413768i
$807$	−0.722530	−	13.3118i	−0.0254343	−	0.468596i
$808$	−0.661912	−	1.14646i	−0.0232860	−	0.0403325i
$809$	−4.95952	−	8.59014i	−0.174367	−	0.302013i	0.765575	−	0.643347i	$-0.222455\pi$
$809$	−4.95952	−	8.59014i	−0.174367	−	0.302013i	−0.939942	+	0.341334i	$0.889121\pi$
$810$	−7.23761	−	32.8439i	−0.254304	−	1.15402i
$811$		−	47.8705i		−	1.68096i	−0.541841	−	0.840481i	$-0.682273\pi$
$811$		−	47.8705i		−	1.68096i	0.541841	−	0.840481i	$-0.317727\pi$
$812$	−20.0487	+	4.15526i	−0.703573	+	0.145821i
$813$	4.80692	−	3.13441i	0.168586	−	0.109928i
$814$	−8.58284	−	0.154792i	−0.300828	−	0.00542546i
$815$	4.98649	−	2.87895i	0.174669	−	0.100845i
$816$	−0.722045	+	1.42365i	−0.0252766	+	0.0498377i
$817$	−5.25633	+	9.10424i	−0.183896	+	0.318517i
$818$			11.8764i			0.415248i
$819$	−11.3353	−	35.0469i	−0.396087	−	1.22464i
$820$		−	15.3384i		−	0.535639i
$821$	14.3341	−	24.8274i	0.500264	−	0.866482i	−0.499736	−	0.866178i	$-0.666570\pi$
$821$	14.3341	−	24.8274i	0.500264	−	0.866482i	1.00000		0.000304753i	$-9.70060e-5\pi$
$822$	19.9654	+	10.1260i	0.696373	+	0.353186i
$823$	20.0175	+	34.6713i	0.697766	+	1.20857i	0.969239	+	0.246120i	$0.0791556\pi$
$823$	20.0175	+	34.6713i	0.697766	+	1.20857i	−0.271474	+	0.962446i	$0.587511\pi$
$824$	−4.94954	+	8.57285i	−0.172425	+	0.298649i
$825$	24.1173	−	45.4989i	0.839655	−	1.58407i
$826$	−22.2095	−	7.34113i	−0.772768	−	0.255431i
$827$	5.40955			0.188109			0.0940543	−	0.995567i	$-0.470017\pi$
$827$	5.40955			0.188109			0.0940543	+	0.995567i	$0.470017\pi$
$828$	13.8194	−	10.1194i	0.480259	−	0.351672i
$829$	4.25136	+	7.36358i	0.147656	+	0.255748i	0.930361	−	0.366646i	$-0.119494\pi$
$829$	4.25136	+	7.36358i	0.147656	+	0.255748i	−0.782705	+	0.622393i	$0.786160\pi$
$830$	−41.0301	+	23.6887i	−1.42418	+	0.822248i
$831$	0.840994	+	15.4943i	0.0291738	+	0.537492i
$832$			4.64070i			0.160887i
$833$	0.739429	−	6.40879i	0.0256197	−	0.222051i
$834$	11.7353	−	7.65216i	0.406361	−	0.264973i
$835$	33.0765	+	19.0967i	1.14466	+	0.660870i
$836$	13.5998	+	8.18230i	0.470357	+	0.282991i
$837$	−8.33447	−	10.1753i	−0.288081	−	0.351710i
$838$	18.6690	+	10.7785i	0.644910	+	0.372339i
$839$			6.66926i			0.230248i	0.993351	+	0.115124i	$0.0367266\pi$
$839$			6.66926i			0.230248i	−0.993351	+	0.115124i	$0.963273\pi$
$840$	−4.37902	−	16.5551i	−0.151091	−	0.571207i
$841$	30.8883			1.06511
$842$	6.08439	−	10.5385i	0.209682	−	0.363180i
$843$	17.9785	−	35.4480i	0.619212	−	1.22089i
$844$	−15.4275	+	8.90708i	−0.531037	+	0.306594i
$845$	−27.6247	−	15.9491i	−0.950317	−	0.548666i
$846$	15.7272	+	6.93206i	0.540714	+	0.238329i
$847$	−28.6921	+	4.87494i	−0.985871	+	0.167505i
$848$			3.81124i			0.130879i
$849$	−2.43536	−	44.8687i	−0.0835815	−	1.53989i
$850$	−4.13078	−	7.15472i	−0.141685	−	0.245405i
$851$	12.7976	−	7.38871i	0.438697	−	0.253282i
$852$	−1.07934	−	19.8856i	−0.0369776	−	0.681268i
$853$			14.2558i			0.488109i	0.969761	+	0.244055i	$0.0784776\pi$
$853$			14.2558i			0.488109i	−0.969761	+	0.244055i	$0.921522\pi$
$854$	4.04708	+	19.5268i	0.138488	+	0.668192i
$855$	−21.6375	+	49.0905i	−0.739988	+	1.67886i
$856$	−5.61684	+	9.72865i	−0.191980	+	0.332518i
$857$	18.2335	+	31.5813i	0.622844	+	1.07880i	0.988954	+	0.148225i	$0.0473561\pi$
$857$	18.2335	+	31.5813i	0.622844	+	1.07880i	−0.366110	+	0.930572i	$0.619311\pi$
$858$	0.964605	+	26.6413i	0.0329311	+	0.909520i
$859$	−10.1170	+	17.5232i	−0.345189	+	0.597884i	−0.985388	−	0.170325i	$-0.945518\pi$
$859$	−10.1170	+	17.5232i	−0.345189	+	0.597884i	0.640199	+	0.768209i	$0.278852\pi$
$860$	−8.20919			−0.279931
$861$	−13.2576	−	13.3430i	−0.451819	−	0.454730i
$862$	−13.5244			−0.460644
$863$	6.55825	+	3.78641i	0.223245	+	0.128891i	0.607452	−	0.794356i	$-0.292192\pi$
$863$	6.55825	+	3.78641i	0.223245	+	0.128891i	−0.384207	+	0.923247i	$0.625525\pi$
$864$	3.29258	+	4.01981i	0.112016	+	0.136757i
$865$	22.6381	−	13.0701i	0.769719	−	0.444397i
$866$	−17.1658	+	29.7321i	−0.583318	+	1.01034i
$867$	−15.2793	−	23.4323i	−0.518912	−	0.795802i
$868$	−4.45596	−	4.99964i	−0.151245	−	0.169699i
$869$	−49.9561	+	27.6533i	−1.69464	+	0.938073i
$870$	2.71470	+	50.0151i	0.0920370	+	1.69567i
$871$	−3.13790	+	1.81167i	−0.106324	+	0.0613860i
$872$	−3.95986	+	2.28623i	−0.134098	+	0.0774215i
$873$	21.5672	+	29.4531i	0.729938	+	0.996835i
$874$	−27.3221			−0.924183
$875$	37.2134	+	12.3005i	1.25804	+	0.415833i
$876$	15.6717	−	10.2189i	0.529499	−	0.345266i
$877$	33.6074	+	19.4033i	1.13484	+	0.655202i	0.945148	−	0.326641i	$-0.105917\pi$
$877$	33.6074	+	19.4033i	1.13484	+	0.655202i	0.189694	+	0.981843i	$0.439250\pi$
$878$	2.95877	−	1.70824i	0.0998536	−	0.0576505i
$879$	−4.36153	+	8.59960i	−0.147111	+	0.290057i
$880$	−0.223487	+	12.3918i	−0.00753374	+	0.417727i
$881$			38.0866i			1.28317i	0.767052	+	0.641584i	$0.221723\pi$
$881$			38.0866i			1.28317i	−0.767052	+	0.641584i	$0.778277\pi$
$882$	−18.1187	−	10.6166i	−0.610090	−	0.357478i
$883$	17.6201			0.592964			0.296482	−	0.955038i	$-0.404187\pi$
$883$	17.6201			0.592964			0.296482	+	0.955038i	$0.404187\pi$
$884$	3.70394	+	2.13847i	0.124577	+	0.0719245i
$885$	−25.8839	+	51.0350i	−0.870077	+	1.71552i
$886$	−21.5391	+	12.4356i	−0.723622	+	0.417783i
$887$	13.6872	−	23.7070i	0.459572	−	0.796002i	−0.539366	−	0.842071i	$-0.681336\pi$
$887$	13.6872	−	23.7070i	0.459572	−	0.796002i	0.998938	+	0.0460690i	$0.0146694\pi$
$888$	2.44861	+	3.75518i	0.0821699	+	0.126015i
$889$	12.9339	+	4.27518i	0.433790	+	0.143385i
$890$	32.1455			1.07752
$891$	19.7376	+	22.3926i	0.661235	+	0.750179i
$892$	−4.55482	−	7.88917i	−0.152507	−	0.264149i
$893$	−13.7080	−	23.7430i	−0.458721	−	0.794528i
$894$	22.8317	−	1.23925i	0.763608	−	0.0414468i
$895$	−86.6027			−2.89481
$896$	1.76035	+	1.97514i	0.0588092	+	0.0659846i
$897$	−25.0663	−	38.4416i	−0.836939	−	1.28353i
$898$	−10.6050	−	6.12283i	−0.353895	−	0.204321i
$899$	9.79450	+	16.9646i	0.326665	+	0.565800i
$900$	−26.7347	+	2.91076i	−0.891156	+	0.0970255i
$901$	3.04191	+	1.75625i	0.101341	+	0.0585092i
$902$	6.59301	+	11.9104i	0.219523	+	0.396572i
$903$	−7.14129	+	7.09558i	−0.237647	+	0.236126i
$904$		−	7.52223i		−	0.250186i
$905$	−20.5223	−	11.8485i	−0.682184	−	0.393859i
$906$	−18.3957	−	9.32993i	−0.611157	−	0.309966i
$907$	−6.46073	−	11.1903i	−0.214525	−	0.371568i	0.738600	−	0.674143i	$-0.235487\pi$
$907$	−6.46073	−	11.1903i	−0.214525	−	0.371568i	−0.953126	+	0.302575i	$0.902154\pi$
$908$	12.5369	−	21.7145i	0.416050	−	0.720620i
$909$	−1.60180	+	3.63412i	−0.0531284	+	0.120536i
$910$	−44.9270	+	9.31149i	−1.48932	+	0.308673i
$911$		−	2.02350i		−	0.0670416i	−0.999438	−	0.0335208i	$-0.989328\pi$
$911$		−	2.02350i		−	0.0670416i	0.999438	−	0.0335208i	$-0.0106720\pi$
$912$	−0.449224	−	8.27642i	−0.0148753	−	0.274060i
$913$	21.6779	−	36.0308i	0.717435	−	1.19245i
$914$	−26.7154	+	15.4241i	−0.883667	+	0.510185i
$915$	48.7129	−	2.64402i	1.61040	−	0.0874086i
$916$	−23.1049			−0.763408
$917$	27.8586	+	31.2576i	0.919972	+	1.03222i
$918$	4.72563	−	0.775587i	0.155969	−	0.0255982i
$919$	23.8097	+	13.7465i	0.785410	+	0.453457i	0.838344	−	0.545141i	$-0.183524\pi$
$919$	23.8097	+	13.7465i	0.785410	+	0.453457i	−0.0529342	+	0.998598i	$0.516857\pi$
$920$	−10.6677	−	18.4770i	−0.351704	−	0.609170i
$921$	46.6616	+	23.6658i	1.53755	+	0.779814i
$922$	1.70165	−	2.94734i	0.0560408	−	0.0970655i
$923$	−53.3580			−1.75630
$924$	10.5164	+	10.9730i	0.345963	+	0.360984i
$925$	−23.2016			−0.762864
$926$	7.91328	−	13.7062i	0.260046	−	0.450414i
$927$	29.5228	−	3.21432i	0.969655	−	0.105572i
$928$	−3.86938	−	6.70196i	−0.127018	−	0.220002i
$929$	−16.7462	−	9.66845i	−0.549426	−	0.317212i	0.199464	−	0.979905i	$-0.436080\pi$
$929$	−16.7462	−	9.66845i	−0.549426	−	0.317212i	−0.748891	+	0.662694i	$0.769413\pi$
$930$	−13.7238	+	8.94877i	−0.450022	+	0.293442i
$931$	13.3136	+	30.7386i	0.436334	+	1.00742i
$932$	23.2786			0.762517
$933$	0.0859678	+	1.58385i	0.00281446	+	0.0518530i
$934$	−18.9467	+	10.9389i	−0.619956	+	0.357932i
$935$	9.78742	+	5.88860i	0.320083	+	0.192578i
$936$	11.2326	−	8.22514i	0.367150	−	0.268847i
$937$			6.07745i			0.198542i	0.995060	+	0.0992708i	$0.0316510\pi$
$937$			6.07745i			0.198542i	−0.995060	+	0.0992708i	$0.968349\pi$
$938$	−0.648309	+	1.96136i	−0.0211680	+	0.0640408i
$939$	−5.44156	−	8.34516i	−0.177579	−	0.272334i
$940$	10.7044	−	18.5406i	0.349139	−	0.604726i
$941$	1.16233	+	2.01322i	0.0378910	+	0.0656292i	0.884349	−	0.466826i	$-0.154603\pi$
$941$	1.16233	+	2.01322i	0.0378910	+	0.0656292i	−0.846458	+	0.532456i	$0.821269\pi$
$942$	−9.47957	+	18.6908i	−0.308861	+	0.608978i
$943$	−20.2952	−	11.7175i	−0.660904	−	0.381573i
$944$		−	8.84110i		−	0.287753i
$945$	−32.3097	+	39.9415i	−1.05103	+	1.29930i
$946$	6.37452	−	3.52862i	0.207253	−	0.114725i
$947$	−7.66708	−	4.42659i	−0.249147	−	0.143845i	0.370227	−	0.928941i	$-0.379280\pi$
$947$	−7.66708	−	4.42659i	−0.249147	−	0.143845i	−0.619374	+	0.785096i	$0.712613\pi$
$948$	26.5942	+	13.4880i	0.863739	+	0.438070i
$949$	−25.0637	−	43.4116i	−0.813603	−	1.40920i
$950$	37.1504	+	21.4488i	1.20532	+	0.695891i
$951$	−15.2346	+	9.93393i	−0.494017	+	0.322130i
$952$	2.38762	−	0.494854i	0.0773833	−	0.0160383i
$953$	15.5373			0.503303			0.251651	−	0.967818i	$-0.419026\pi$
$953$	15.5373			0.503303			0.251651	+	0.967818i	$0.419026\pi$
$954$	9.22496	−	6.75503i	0.298669	−	0.218702i
$955$	13.1367	+	22.7534i	0.425092	+	0.736281i
$956$	1.47636	+	2.55714i	0.0477490	+	0.0827038i
$957$	−23.6064	−	37.6703i	−0.763086	−	1.21771i
$958$	24.5435			0.792965
$959$	−6.93988	−	33.4843i	−0.224101	−	1.08126i
$960$	5.42167	−	3.53527i	0.174984	−	0.114100i
$961$	12.2963	−	21.2978i	0.396655	−	0.687026i
$962$	10.4021	−	6.00563i	0.335376	−	0.193629i
$963$	33.5030	−	3.64768i	1.07962	−	0.117545i
$964$	−3.18416	−	1.83837i	−0.102555	−	0.0592100i
$965$	−32.5706			−1.04848
$966$	−25.2505	−	6.85282i	−0.812423	−	0.220486i
$967$		−	50.7815i		−	1.63302i	−0.577329	−	0.816512i	$-0.695905\pi$
$967$		−	50.7815i		−	1.63302i	0.577329	−	0.816512i	$-0.304095\pi$
$968$	−5.15292	−	9.71841i	−0.165621	−	0.312361i
$969$	−6.81276	−	3.45529i	−0.218857	−	0.111000i
$970$	39.3796	−	22.7358i	1.26440	−	0.730004i
$971$	−31.0032	−	17.8997i	−0.994941	−	0.574429i	−0.0881935	−	0.996103i	$-0.528109\pi$
$971$	−31.0032	−	17.8997i	−0.994941	−	0.574429i	−0.906748	+	0.421674i	$0.861443\pi$
$972$	3.89404	−	15.0943i	0.124901	−	0.484148i
$973$	−20.3190	−	6.71625i	−0.651399	−	0.215313i
$974$	36.1783			1.15923
$975$	3.90516	+	71.9478i	0.125065	+	2.30417i
$976$	−6.52747	+	3.76863i	−0.208939	+	0.120631i
$977$	−15.2247	+	8.79000i	−0.487082	+	0.281217i	−0.723363	−	0.690468i	$-0.757405\pi$
$977$	−15.2247	+	8.79000i	−0.487082	+	0.281217i	0.236281	+	0.971685i	$0.424071\pi$
$978$	2.66488	−	0.144643i	0.0852135	−	0.00462519i
$979$	−24.9613	+	13.8174i	−0.797766	+	0.441604i
$980$	−15.5893	+	21.0052i	−0.497983	+	0.670987i
$981$	12.5522	+	5.53259i	0.400760	+	0.176642i
$982$	19.8330	−	34.3518i	0.632896	−	1.09621i
$983$	31.5232	−	18.1999i	1.00543	−	0.580487i	0.0955818	−	0.995422i	$-0.469529\pi$
$983$	31.5232	−	18.1999i	1.00543	−	0.580487i	0.909851	+	0.414935i	$0.136196\pi$
$984$	3.21577	−	6.34050i	0.102515	−	0.202128i
$985$	1.80181	+	1.04028i	0.0574105	+	0.0331460i
$986$	−7.13215			−0.227134
$987$	−6.71356	−	25.3810i	−0.213695	−	0.807885i
$988$	−22.2077			−0.706522
$989$	−6.27127	+	10.8622i	−0.199415	+	0.345396i
$990$	30.3899	−	21.4222i	0.965855	−	0.680842i
$991$	4.46111	+	7.72687i	0.141712	+	0.245452i	0.928141	−	0.372228i	$-0.121406\pi$
$991$	4.46111	+	7.72687i	0.141712	+	0.245452i	−0.786429	+	0.617680i	$0.788073\pi$
$992$	1.26564	−	2.19216i	0.0401842	−	0.0696011i
$993$	−14.2695	−	21.8837i	−0.452830	−	0.694459i
$994$	−22.7098	+	20.2402i	−0.720310	+	0.641981i
$995$			24.2052i			0.767355i
$996$	−21.9273	+	1.19016i	−0.694793	+	0.0377117i
$997$	−0.0417701	+	0.0241160i	−0.00132287	+	0.000763761i	−0.500661	−	0.865643i	$-0.666910\pi$
$997$	−0.0417701	+	0.0241160i	−0.00132287	+	0.000763761i	0.499338	+	0.866407i	$0.333576\pi$
$998$	−16.0605	−	27.8176i	−0.508386	−	0.880550i
$999$	4.74935	−	12.5824i	0.150263	−	0.398090i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.n.e.65.9	yes	24
3.2	odd	2		462.2.n.f.65.1	yes	24
7.4	even	3	inner	462.2.n.e.263.1	yes	24
11.10	odd	2		462.2.n.f.65.9	yes	24
21.11	odd	6		462.2.n.f.263.9	yes	24
33.32	even	2	inner	462.2.n.e.65.1	✓	24
77.32	odd	6		462.2.n.f.263.1	yes	24
231.32	even	6	inner	462.2.n.e.263.9	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.n.e.65.1	✓	24	33.32	even	2	inner
462.2.n.e.65.9	yes	24	1.1	even	1	trivial
462.2.n.e.263.1	yes	24	7.4	even	3	inner
462.2.n.e.263.9	yes	24	231.32	even	6	inner
462.2.n.f.65.1	yes	24	3.2	odd	2
462.2.n.f.65.9	yes	24	11.10	odd	2
462.2.n.f.263.1	yes	24	77.32	odd	6
462.2.n.f.263.9	yes	24	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.783456 - 1.54473i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.23623 + 1.86844i) q^{5} +(0.946049 + 1.45086i) q^{6} +(0.830341 - 2.51208i) q^{7} +1.00000 q^{8} +(-1.77239 - 2.42046i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.783456 - 1.54473i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(3.23623 + 1.86844i) q^{5} +(0.946049 + 1.45086i) q^{6} +(0.830341 - 2.51208i) q^{7} +1.00000 q^{8} +(-1.77239 - 2.42046i) q^{9} +(-3.23623 + 1.86844i) q^{10} +(1.70984 - 2.84191i) q^{11} +(-1.72951 + 0.0938734i) q^{12} +4.64070i q^{13} +(1.76035 + 1.97514i) q^{14} +(5.42167 - 3.53527i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.460807 + 0.798142i) q^{17} +(2.98238 - 0.324709i) q^{18} +(-4.14430 - 2.39271i) q^{19} -3.73687i q^{20} +(-3.22995 - 3.25076i) q^{21} +(1.60625 + 2.90172i) q^{22} +(-4.94452 - 2.85472i) q^{23} +(0.783456 - 1.54473i) q^{24} +(4.48211 + 7.76324i) q^{25} +(-4.01896 - 2.32035i) q^{26} +(-5.12755 + 0.841552i) q^{27} +(-2.59069 + 0.536942i) q^{28} +7.73875 q^{29} +(0.350793 + 6.46294i) q^{30} +(1.26564 + 2.19216i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.05041 - 4.86775i) q^{33} -0.921615 q^{34} +(7.38083 - 6.57821i) q^{35} +(-1.20998 + 2.74517i) q^{36} +(-1.29412 + 2.24149i) q^{37} +(4.14430 - 2.39271i) q^{38} +(7.16863 + 3.63578i) q^{39} +(3.23623 + 1.86844i) q^{40} +4.10460 q^{41} +(4.43021 - 1.17184i) q^{42} -2.19681i q^{43} +(-3.31609 - 0.0598058i) q^{44} +(-1.21340 - 11.1448i) q^{45} +(4.94452 - 2.85472i) q^{46} +(4.96151 + 2.86453i) q^{47} +(0.946049 + 1.45086i) q^{48} +(-5.62107 - 4.17176i) q^{49} -8.96422 q^{50} +(1.59394 - 0.0865151i) q^{51} +(4.01896 - 2.32035i) q^{52} +(3.30063 - 1.90562i) q^{53} +(1.83497 - 4.86137i) q^{54} +(10.8433 - 6.00235i) q^{55} +(0.830341 - 2.51208i) q^{56} +(-6.94298 + 4.52725i) q^{57} +(-3.86938 + 6.70196i) q^{58} +(-7.65662 + 4.42055i) q^{59} +(-5.77247 - 2.92767i) q^{60} +(6.52747 + 3.76863i) q^{61} -2.53129 q^{62} +(-7.55207 + 2.44259i) q^{63} +1.00000 q^{64} +(-8.67085 + 15.0184i) q^{65} +(5.74080 - 0.207858i) q^{66} +(0.390387 + 0.676170i) q^{67} +(0.460807 - 0.798142i) q^{68} +(-8.28358 + 5.40141i) q^{69} +(2.00648 + 9.68109i) q^{70} +11.4978i q^{71} +(-1.77239 - 2.42046i) q^{72} +(-9.35455 + 5.40085i) q^{73} +(-1.29412 - 2.24149i) q^{74} +(15.5037 - 0.841502i) q^{75} +4.78543i q^{76} +(-5.71935 - 6.65500i) q^{77} +(-6.73300 + 4.39033i) q^{78} +(-14.9095 - 8.60802i) q^{79} +(-3.23623 + 1.86844i) q^{80} +(-2.71724 + 8.58001i) q^{81} +(-2.05230 + 3.55469i) q^{82} +12.6784 q^{83} +(-1.20026 + 4.42260i) q^{84} +3.44396i q^{85} +(1.90249 + 1.09840i) q^{86} +(6.06297 - 11.9543i) q^{87} +(1.70984 - 2.84191i) q^{88} +(-7.44976 - 4.30112i) q^{89} +(10.2583 + 4.52155i) q^{90} +(11.6578 + 3.85336i) q^{91} +5.70943i q^{92} +(4.37787 - 0.237621i) q^{93} +(-4.96151 + 2.86453i) q^{94} +(-8.94127 - 15.4867i) q^{95} +(-1.72951 + 0.0938734i) q^{96} -12.1684 q^{97} +(6.42339 - 2.78211i) q^{98} +(-9.90923 + 0.898400i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 8 q^{9}+O(q^{10}) \) 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 8 * q^9	\( 24 q - 12 q^{2} - 12 q^{4} + 24 q^{8} - 8 q^{9} - 4 q^{11} + 4 q^{15} - 12 q^{16} + 4 q^{17} - 8 q^{18} + 8 q^{22} + 20 q^{25} - 12 q^{27} + 40 q^{29} - 2 q^{30} - 28 q^{31} - 12 q^{32} + 32 q^{33} - 8 q^{34} - 32 q^{35} + 16 q^{36} - 16 q^{37} - 8 q^{41} + 6 q^{42} - 4 q^{44} - 28 q^{45} - 8 q^{49} - 40 q^{50} - 34 q^{51} + 6 q^{54} + 8 q^{55} + 40 q^{57} - 20 q^{58} - 2 q^{60} + 56 q^{62} - 14 q^{63} + 24 q^{64} - 44 q^{65} + 32 q^{66} + 4 q^{68} - 20 q^{69} + 64 q^{70} - 8 q^{72} - 16 q^{74} - 26 q^{75} + 24 q^{81} + 4 q^{82} + 144 q^{83} - 6 q^{84} + 8 q^{87} - 4 q^{88} + 56 q^{90} - 32 q^{91} - 22 q^{93} - 44 q^{95} + 64 q^{97} - 8 q^{98} - 52 q^{99}+O(q^{100}) \) 24 * q - 12 * q^2 - 12 * q^4 + 24 * q^8 - 8 * q^9 - 4 * q^11 + 4 * q^15 - 12 * q^16 + 4 * q^17 - 8 * q^18 + 8 * q^22 + 20 * q^25 - 12 * q^27 + 40 * q^29 - 2 * q^30 - 28 * q^31 - 12 * q^32 + 32 * q^33 - 8 * q^34 - 32 * q^35 + 16 * q^36 - 16 * q^37 - 8 * q^41 + 6 * q^42 - 4 * q^44 - 28 * q^45 - 8 * q^49 - 40 * q^50 - 34 * q^51 + 6 * q^54 + 8 * q^55 + 40 * q^57 - 20 * q^58 - 2 * q^60 + 56 * q^62 - 14 * q^63 + 24 * q^64 - 44 * q^65 + 32 * q^66 + 4 * q^68 - 20 * q^69 + 64 * q^70 - 8 * q^72 - 16 * q^74 - 26 * q^75 + 24 * q^81 + 4 * q^82 + 144 * q^83 - 6 * q^84 + 8 * q^87 - 4 * q^88 + 56 * q^90 - 32 * q^91 - 22 * q^93 - 44 * q^95 + 64 * q^97 - 8 * q^98 - 52 * q^99

Introduction

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